My soon-to-be wife and I are in a similar situation. She is currently in Canada as a visitor and we are planning to get married later this month (August). My questions are:
1. What does UCI mean ? (box 1)
It's your Client ID number- if you don't have one, CIC will provide you one eventually.
2. What to select in box 3 ? All 3 options (Extension of my temporary resident status, Initial temporary resident permit or extension of temporary resident permit, Restoration of temporary resident status as a visitor) sound very much the same to me.
That depends on what you're applying for. What is it? Extension is in case you already have one.
3. Where to send the form once we are ready? We live in a small town in rural BC. There are Service Canada and Service BC offices close by but not much else.
Are you applying within Canada? Then...
CPC Vegreville
Permanent Residence Applications
6212-55th Avenue
Vegreville, AB
T9C 1W3
Make sure you have all the forms ready and good luck!
http://www.cic.gc.ca/english/information/applications/index.asp?q=sponsorFam#sponsorFam