Is there some way to heal others?

Go to a Chapel, and buy a convalescence spell, they cost a lot of magicka, but will have to do until you enter the Arcane University, and can make your own.
This can be a pain, as the spell vendor in each chapel only shows up at certain times, I have had to use the wait function. At the same time, buy the restore attribute spell( restore strength or speed or whatever )they sell, and maybe a respite( restore fatigue spell ).

As Zen said, a good way is to buy a Convalescence spell. However, if you have Frostcrag Spire OR access to the Arcane University, you could make your own spell to heal others.

Dont asking for to muc spoilers, but what is the Arcane University, do i need some quest to access it? Its in the capitol right?

Join the mages guild at any hall, Teekeus in Chorrol will do, then you have to do a quest at each of the local guilds at the other towns. Once all are completed, you can enter the university. Worth it as the services this gives you access to are awesome

I wish there were more people to Heal.

My character only has healing skill as main skills, but i use summoning and now a little mysticism, would that be enough to join hte mage guild?

Sadly enough, you can go through the entire Mage's Guild quest without using a single spell. Actually specializing in any of the magical schools is just a bonus really.

I wish the people you have to keep alive weren't so stupid, personally.

Not to spoil the main quest too much but there's one particular level where there's a Dark Elf knight who isn't very bright. You have to keep him alive to get the good reward for the quest. He has a tendency to fall off bridges into rivers of lava, or rush head long into room fulls of Daedra.

Well not quite, there is one mission where you need to cast four spells. But I agree that the missions should be more focused on using spells than just doing so many missions that could be in the fighters guild, if it weren't for the dialogue.

That depends whether you count using a scroll as casting a spell. Personally I don't, because scrolls don't require any magic skill.