How to apply for a university after immigrating to Canada?

Applying for a university has nothing to do with immigration. As long as you meet the requirements for university entrance, you can apply for a university. Canadian universities accept IELTS and TOEFL, or MELAB, COPE and so on. Apply for university to go to official website.

Broaden your circle of friends. In fact, you will meet many people in your class. Or you can meet people outside, the key depends on your own communication skills.

Immigration, wait until you get the maple leaf card. Right is basically what you said.

If you are looking for a part-time job, just meet the conditions and age. But some schools don't necessarily allow students to go out and find part-time jobs (I'm not sure about the details), so it's better to find part-time jobs.