1. is perfect. Other options: "Please could you resolve the problem soon." "I would appreciate it if you could resolve this problem soon."
("solve a problem" is wrong here - "solve" is for problems requiring logic or specialist knowledge. "resolve" is for problems between people.)
2. "How can I make a complaint, please?" "What is your complaints procedure?" Every organisation has a different system for complaints. If there is no system, you could ask: "Who can I complain to? What is their address?" (I've not heard of a "complaints book" in the UK or any other English-speaking country)