Rubiksmoose tells you what the familiar cannot do and Pacattack tells you what the familiar can do (except for using scrolls).
However, the big question is what the familiar will do.
The familiar is an independent entity and is generally smarter than the base animal it comes from. So, it should be able to take most actions that it is physically and mentally capable of and that it wants to do.
If it doesn't have hands, good luck getting a potion bottle out of your pack and feeding it to you. If you can convince you GM how the familiar accomplishes it, great.
As far has a Healing check, figure out if the familiar can actually do something. A familiar with a large enough beak or mouth may be able to remove an arrow. A dog may "lick the wounds" to some dubious benefit. If you can sell it to the GM, great.
It can use any magic device that it can manipulate and that doesn't require something that the familiar doesn't posses (like spell casting capability).
The fallback could just be: go get help.
Now as far as wanting to help, that is another question. The rules state that the familiar must obey commands. However, the spell caster is now unconscious and cannot give commands. So, how does the spell caster treat the familiar? What is the familiar's personality? In general, a dog would be loyal in most circumstances. An avian might take a wait and see attitude: "if he's strong, he'll get back up and be worth continuing to follow." A cat would be a bit random: "he didn't give me snacks this morning so no help from me. That's teach him!"
So, as long as the familiar can physically help and and wants to help, the familiar will aid the spell caster.