Ships & Modules

I used to run 5-6/10s for Guristas in a Tengu alot. However this was before the addition of missile guidance modules. You've got alot of questions so let me try answer them as best I can

1. HAMs are definitely the way to go, the range required in these sites aren't that far and HMs simply don't have the damage to do them in a decent time. You probably only 'need' 300 or so dps to do a 5-6/10 for Guristas since there aren't any rats that have a msasive tank or anything, but you obviously want more to do them in a reasonable time. The Tengu I used to run had a little over 900 dps and could do a 6/10 in like 15-20mins IIRC (5/10s take longer). As for ammo required, I used to bring all 3, faction, rage and javelin and switch accordingly. However faction and rage was what I used most. Javelin is only required in the last room of the 5/10 where there are 2 web towers that web @ 50+km. However you can get around this by just killing the final rat, bookmarking the wreck, warping off and coming back. However I didn't like to do that as it opened the possibility of someone ninja'ing your loot after you warp out. I'll go over the best method to increase range in the fit.

2. I'm not exactly sure what dps tank number is required, but you are correct that when you're ABing, the battleships in the DEDs won't really hit you which takes a huge chunk of dps off your back. There are also no webs in Guristas 5-6/10s except for the final room of the 5/10.

3. There are no elite frigs and no spider drones in Guristas 5-6/10s so none of this is required. Also as long as they are in range, you will always do roughly the same damage to frigs when using missiles.

After playing with my old fit here's what I'd use if I were still doing these sites today:

[Tengu, Unnamed loadout]
Ballistic Control System II
Ballistic Control System II
Ballistic Control System II
Ballistic Control System II

10MN Afterburner II
Pithum C-Type Medium Shield Booster
Kinetic Deflection Field II
Kinetic Deflection Field II
Missile Guidance Computer II, Missile Range Script
Missile Guidance Computer II, Missile Range Script

Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile
Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile
Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile
Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile
Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile
Heavy Assault Missile Launcher II, Scourge Rage Heavy Assault Missile

Medium Capacitor Control Circuit II
Medium Capacitor Control Circuit I
Medium Hydraulic Bay Thrusters II

Tengu Defensive - Amplification Node
Tengu Electronics - Dissolution Sequencer
Tengu Propulsion - Fuel Catalyst
Tengu Offensive - Accelerated Ejection Bay
Tengu Engineering - Augmented Capacitor Reservoir

It's almost cap-stable (like 6 mins of cap or something which is more than enough). It has a 700dps tank against Guristas which is more than enough as long as you keep your speed up. It puts out 886dps @ 43km with rage, 754dps @ 52km with Faction and 590dps @ 77km with Javelin. Now when I used to run these sites my tactics were as follows:

1. Start with faction ammo, kill all the frigates/dessies. Frigs took 2 volleys and dessies took 1. However this changes with the guidance computers, now I would start with faction ammo (and precision scripts) and that would hopefully allow to 1 shot frigs which will save a TON of time.
2. Once frigs are cleared I'd clear cruisers with faction ammo. Once again this changes since with precision scripts, you should be able to use rage ammo on cruisers for full damage.
3. Finally Battlecruisers then Battleships with rage ammo and range scripts to make sure that you're always in range of the next rat when one goes down. I used to do this with only 30+km range with rage, but now with the range scripts you can hit out to 43km with rage which should make it much easier to ensure you're never burning into range of the next target and wasting time.

Some extra notes, if you find that you don't need the second missile guidance computer (i.e. you can 1 shot frigs with just 1 computer and don't need the extra range) then you should consider an ECCM module. Sometimes you can get really unlucky with jamming battleship rat spawns which cuts into your completion time alot if you get jammed multiple times in a row. ECCM helps alot with this.

Hope this helps and sorry for the wall of text.

I recently purchased a Tengu for Sansha DED sites in low sec, and I found a good fit in this blog post. I modified it a bit in order to make it cheaper, but it works great. I use T2 BCS instead of faction ones, and switched the Cap recharger for a Missile Guidance Computer II with either range or precision script.
From my experience so far:

1.) Fit for max. dps, meaning 6 launchers and 4 BCS II, use 3-4 med slots for tank (1 medium shield booster, preferably a deadspace one, 1 shield boost amp, 2 slots for faction specific resist/anti-ewar modules, e.g. sensor boosters against serpentis, eccm vs. guristas). You should be cap stable with everything active but the shield booster, you only need to pulse that one if needed.
I use javelins with a precision script vs. frigates, and once they're gone, I switch to rage missiles and a range script for cruisers and larger.

2.) Yes, a Tengu mostly uses its low sig radius to mitigate damage, you won't have the shield booster running permanently except for the last room in 5/10s due to the web towers. Frigs and cruisers do the most damage at close range in each room (cause they hit you best), and they die first. Once only the battleships remain, the incoming damage is quite low. If I had to guess, I'd say most of the times 200ish dps permatank would be enough to run all but the last room. You need a much higher tank there, since you will usually blitz this one (in 5/10s you can destroy the web towers to lower incoming dps, it really depends on your tank and experience whether this is required or not. Otherwise you always aim straight for the overseer and ignore all the other ships, bookmark his wreck, and warp out).

3.) Afaik there are neither elite frigates nor spider drones in 5/10 and 6/10 DED sites. A missile guidance computer or a PWNAGE can be helpful against frigates, but is not required. If you go against guristas or serpentis, anti-ewar is a good option in order to compensate either sensor dampening when fighting serpentis or prevent getting jammed by guristas.

What about running Guristas 7-10/10 DEDs in Tengu? Is it significantly more challenging than Guristas 5-6/10 DEDs?

In regards to the ECCM module, cap friendly is one thing, but the main thing is that you should increase your racial sensor strength (Gravimetric for the Tengu). The multispec ECCM is a straight up useless module.

Now for 7-8/10s. They aren't that much more challenging, you might need a little more tank in some, it's been awhile but I do recall the last room of the 7 or 8 has a 'commander' battleship that webs as well as a lot of dps on field. The issue with 7-8/10s is that they take AGES to do solo. There are a ton of battleships so you have to burn through an obscene amount of EHP to finish the sites. Now this would be fine and dandy if the modules were good, but alas, battleship sized Guristas modules (Pith Hardeners, Pith Large/XL Shield Boosters) are much much cheaper than their medium sized counterparts. So basically all the good loot from Guristas comes from the 5-6/10s. Even Rattlesnake BPCs are dirt cheap relative to other pirate Battleships. So you're spending way more time for a crappier pay out.

However most people know this so 6/10s are very sought after, if you can't find any 7-8/10s are doable in that fit, like I said you might need a little more tank (just drop some missile guidance enhancers) to run em but they're still trivial.

Now the 10/10 is a whole different beast all together.

In a medium shield boosted Tengu ensure you destroy web towers first or your tank will break unless you have some very bling fit.

The problem with gurista lowsec ded sites is that everyone knows they are very good isk. so you will get chased, ganked and spend quite a lot of timing losing the site.

In some regions every single one is prescanned and nothing can safe you if you enter, bar constant combat probe scanning (due to recons not showing on dscan).

I know 6/10s are, not sure about 5s. However they are much less common.

Wolf has a really good point though, doing Guristas sites in a PvE fit in lowsec can be extremely challenging. You need to find a quiet system to do the sites in which is hard since most of the lowsec where Guristas spawn is inhabited. If you're playing on peak US TZ then it'll be even harder. It wasn't as bad for me cause I'm on the AU TZ which is much quieter.

Even then I got hunted down alot and eventually joined a pirate corp and did these sites in groups with PvP fits for security =P