1) Everything written for us means Allah has designed the system and nothing can change His system. Allah manages everything. Now Allah has also written for you to have free will. This is part of what he has written for us. So anything we do it’s “written” by God because He let us do it, and He knows of it. But it doesn’t mean that He forces us to do it.
2) Yes Du’as matter and they can change that which is written
Yes, asking Allah for those things makes a big difference. Allah Has written things for us, but He has also given us the chance to change that (not change all of it, but many aspects of it). We have many hadiths about this.
Supplicate sincerely, pay charity, keep ties with your kins, Allah can change it