So I'm not really sure what double casting a conjuration spell does (additionally what the perk that increases the power of double cast does)? Does anyone know for sure? Does it increase durration/the level of the summoned creature

From what I have noticed, it seems to increase the damage output and durability of the summon. Now keep in mind this is while I was in a dungeon so I haven't had the chance to sit down and compare the damage but I typically will dual cast if I am not painfully tight on mana.

It increases the duration of the summon.

That is so lame. Why one earth would I want to spend 2x the magicka to get 2x the durration when I could just cast the spell two times and have a reset of HP on the creature?

Because you can cast the spell well in advance, especially helpful once you can get two summons at once?

I used to double up my conjuration as well, but noticed it almost drained me of all my magicka going into battle. Now, I just single-hand a summon, then I can use destruct or whatever much more efficiently. Also, when you get the perk that enables your summons to last twice as long, you don't need to double-up IMO.

i dual cast if i get the impression that something nasty lurks around the corner, then i head there with my longer lasting summon plus full magic bar due to out of combat quick regen..

dont wanna be double casting mid fight...

but then they last 4x as long...right?

The 2 minute summon duration helps a lot I find if there's a tough battle you need to prepare for. Ill cast my summons, wait for mana, throw up my stoneflesh, wait for mana, put up lightning cloak and then wait for full mana again..

By the time all that is done, if my summon only last 1 minute he would probably only have 30-40 seconds or so left which isn't a lot of time.

I believe so, yes. The only problem i have with dual-casting summons is that they generally tend to die before they time out. so i waste magicka in that aspect. Of course, the strongest summon i have is a flame atronach, soo I guess i can't really complain lol.