Allah swt gives us free will and we choose our own actions. He knows what we will choose but at the end of the day, we chose that. So everything is not predestined.

1) My first question is, when something happens in life, for example getting accepted to a certain university or earning a certain job or having some illness, am I still allowed to say "this is what Allah wants" or "This is what Allah planned" or " Allah made this happen for a reason and because there is some good purpose in it"? Because yes I do believe not everything is predestined obviously but I always end up saying some of these phrases and I dont know if its wrong saying them.

2)My second question is about Qadhaa and Qadr. Can I get the exact definition and some explanation and example.

1) Yes you can say Allah willed for those events because in reality Allah willed to create a system, and he determined its millions of factors, and he willed to create you and he willed to give you free will and you used your free will, and in then end you came to a specific result. That result was written by Allah (and part of Allah’s decree is for you to have free will). So in the end, whatever happened, Allah knew of it and allowed it to happen.

2) As for what is Qadha’ and Qadar, I recommend seeing this video: