1. Not really. That is why you have to show funds when you apply for PR. You do not qualify to get employment insurance until you have worked a certain number of hours. You could apply for welfare if you have no job and no money left but it is not much, about $500 a month from what I have heard so that is not enough to live on.
2. Health care is not tied to being a PR. It is provincial and so it is tied to living in a certain province. There are 4 provinces that have a 3 month waiting period for health care after you land. They are Ontario, BC, NB and QC. If you are planning on settling there, you should get travel insurance for the first 3 months to take care of possible emergencies until you get health care. In other provinces, you can register for health care after you arrive and get it right away.
3. Yes
4. Child tax benefit, see http://www.cra-arc.gc.ca/bnfts/cctb/fq_qlfyng-eng.html