You can not renew your health care as a visitor. Visitors do not qualify for health care :( I do not think you can get EI as a visitor either. You need to talk to Service Canada about this. It's unfair since you've paid into it but they have their rules.
I do not know how fast CEC is, immigration lists no time for it yet, you may be able to find something on trackitt.com/canada-immigration-trackers If you applied under FSW with AEO, I have heard it would be really fast. Your employer could try to get an AEO, they are easier to get than LMO's.
Spousal sponsorship depends on inland or outland. If you apply inland and your application is rock-solid and all the info there and you apply for a work permit at the same time, you could have your work permit in 5-6 months. That would re-instate your health care but I am not sure if it would re-instate your rights to EI maternity benefits. You would have to ask Service Canada about that. You could have your PR in anywhere from 8 months to 2 years. If you apply outland, there is no open work permit but processing time can be fast depending on where your application is processed, see
http://www.cic.gc.ca/english/information/times/international/05-fc-spouses.asp You have to add another month or so to these timelines for sponsor approval in the beginning.