Skill Discussions

Not to start, no. I'd consider level 4 though, especially if you are a shield tanker.

Engineering itself needs to be V. Anything rank 1 or rank 2 in engineering should be V. Check the descriptions of what a skill gives you and see if you need it; you'll probably enjoy 5% more capacitor and 5% faster cap regen, for instance.

Other than to satisfy prerequisites for specific modules/skills- nothing NEEDS to be trained to V. It just makes better use of whatever module it is affected by. There is no list of 'must have to V' skills. Even very rigid fleet set ups like logi support for Incursions simply need to adjust for those with IV in relevant skills (more cap chains to be stable, etc)

Further, what will benefit from V's depends on what you are doing. Again using incursion logi as an example, then certainly Logi itself, Energy Management, Remote Repair, etc all 'should' be V to run at max efficiency, and even having V in say, all the Engineering skills, won't make up for having a IV versus a V in logi or remote repair. Anything running active reps, MWD, or cloaks will always eat up cap, so Engineering becomes a very valuable tree to max if you fly those types of ships/modules. Amarr as well tend to active reps and laser turrets, so cap is at a premium.

One really must weigh the benefits on a per use basis. Would spending two weeks getting 5% more cap be a better investment than the same amount of time for another level in say, a frigate skill that reduces cap usage for weapons by 10%? Depends on what you fly.

In virtually any PvE, it doesn't really matter. You are just less efficient but there isn't much negative impact there. In PvP, then yes, it does matter. 5% can make a difference, but usually it's more generic, such as being able to fit T2 versus T1. More importantly though, you can count on any given PvP opponent to have maxed skills.
In that regard, V's are like any arms race- you are better to have it than not simply because the other guy very well may.

Don't get too bogged down in numbers and levels for PvP however. More is usually better, but PvP entails so much more than comparing EFT stats, that it's extremely rare to be able to say that 'if I had 2% more cap regen, I would have won that fight'

If Engineering itself could be trained to 6, it would need to be. Even noobs should train the Engineering skill itself to 5 within the first couple of monhs of play. The other skillz in the Engineering category can loiter at 4 for quite some time.