Seems like she is always going down at the beginning of battle lol

Shadowmere ftw.

I like that Dark elf mage you get for the azuras star quest.

Does that start of by Azura's shrine because I think I have that in my quest log.

I didn't get that follower (the mage) might be beacuse i chose the black star.

The problem here is that some of the companions features as hit points are fixed the moment you meet them. As Lydia is usually the first companion you meet, she tend to be weaker than others. If you are using the PC version, take all her equipment, send her home, select her in the console, type disable and then enable. This will set all her abilities to your current level.