Can I double cook apple? When making, say, Apple Crumble?
Yes, you can precook most fruit. Apples are among the best fruit to cook like this as they keep some texture after light cooking. (Stone fruit should be OK - I've used plums. Soft fruit much less so). 

If you buy ready made fruit pie filling (and I don't recommend you do) it's precooked. Those of us who grow our own fruit sometimes cook up (and freeze) a batch of pie filling when we have a glut. The main trick is to not precook too much, where "too much" is a matter of taste (some people like mushy fillings; some would rather have a bit of bite) but also depends on the fruit (e.g. the variety of apple) you're starting with. 

Do be careful not to keep it too long after precooking - cooked fruit doesn't keep like fresh fruit and is also more likely to spoil in ways you won't spot. So a few days in the fridge, or freeze it.