Q1: You can mail your permanent resident card to Alberta as long as you claim that you are just transferring from Toronto to Edmonton, and you will be residing in that Edmonton address permanently.
Q2: Getting SIN or not is totally up to you. Just a piece of paper. Most trivial thing. You can do it when you decide to stay in Canada for good.
Q3: CBSA won't check if you have carried sufficient life expense. Their sole concern is if you are carrying some illegal goods and cash over 10000 USD . You can bring 0 to 9999.99 USD cash with you. They will ask you how much cash you are taking with you to see if you are exceeding the 10000 limit.
There's no secret in job searching. Canada is not a wonderland. Employers need talented employees to help them out. Employees need to work hard to be seen, noticed, hired and recognized. It's not something that we can achieve overnight. It's an ongoing process which requires our persistence and focus. All new comers are entitled to same free public resources. Follow all the instructions from those government funded employment agency, keep investing into job searching, you could get a job very soon. Check my previous thread, you can get some ideas.
But I don't think a brief landing can lead you to employment. Offshore applications always end up in vain. Maybe it's a good idea to focus on your current job and get as much money as you can. You are moving to a new country which is more commercialized than China. Money is the key to a happier life here.