Do you get +4 to all of your stats when you fully merge a unit?

Yes

I think so. although I think some units may get +5/+3 because of IV's, but that could be me sucking at math

Yes. You can also double check how the stats will be like for a character by using the FEH unit builder. Just google it.

Yes. Not only good for the obvious reason that higher stats all around is nice, but it helps with arena scoring

Yes, +4 to all stats.

When you +1 a unit it will gain a stat increase in whatever 2 stats was the highest when that unit was lv 1 (not counting weapons and abilities). That means that the unit will get +1 HP (since Hp is always the highest stat at lv1) and +1 whatever was the unit highest stat at lv1. When you +2, the unit will get a bonus to their 3rd and 4rd highest stat, when you +3, the lowest stat and HP... Then it keeps rotating, so at +10 the unit will have received +4 to every stat. By the way, if two stats are equal at lv 1, the priority order is Atk>Spd>Def>Res.

Unlike what bigdingus04 said, getting a unit to +10 can make a big difference. Yeah, you can get similar stats with buffs and skills, but remember that those +4 to every stat will not occupy any slot and will stack with whatever buffs the unit has. To +10 a 5* requires a huge investment though, so make sure that whatever unit you choose to merge is worth the investment.

A cheaper option is to +10 a 4* unit instead. A +10 4* unit will usually be as good as a +5 5*unit. As long as it has the same weapons/skills equipped, of course (which means that, if the unit has an exclusive weapon you will probably want to promote a copy of that unit to 5* in order to inherit it). Also, keep in mind that if you promote your +10 4* unit to +10 it will go back to +0, so DON'T DO THAT.

I personally don't recommend you to +10 a 4* unit if it is top tier since this will limit their growth, but if you have 11 copies of a unit that you don't need for skill inheritance or anything like that and they are just cluttering your box, I might as well merge them. They will probably be more useful than the 200 feathers you can get by selling a 4* unit, which you could just farm anyway...