~We need to refinance~ But we are LOST---

Hi guys,
Im hoping you can help me an my wife  out..... We very new to this, and this is my first time so take it easy on us.

Long story short~
I met my wife a few years back and she was in the middle of a divorce, I moved in to her home that her and her ex had bought. Per her divorce decree she was given the home, (she has owned it for 5 years) and in lieu of child support her ex pays the mortgage. Now this has worked out great, as its a small home and has a small monthly mortgage.

Her ex has brought up the situation a while back that he wanted her to "refinance" the home and have his name removed. He hasnt pushed the issue, as she had to get a new car, bla bla bla- Anyhow we are now wanting to do the refinance and have his name removed from the mortgage.

Here are our questions-
1.- WHERE DO WE START, she works for a bank and has talked to her co-workers about financing there. But hasnt done anything yet. She has decent credit, i do not. She works full time at the bank, I work just shy of full time at my job but am a full time student also.

2.- We are in the position of getting a decent tax return in the next couple weeks and we are going to pay off her little current credit card debt, and place my name as co-borrower on the cards also to increase my credit rating. She currently has a car loan with about 3 years left on it.  Keeping a small debt on one card with both of our names on it is beneficial correct?

3- The house has been financed for 5 years at a fairly high intrest rate. (8%, she claims) Is financing for a 15 year a better route to go? And during the refinance, can we get a little bit extra to help with home upgrades/repairs? If we have to stay at this house for a while, then we need to upgrade a few things- Roof/Fence/Shed/Flooring/Kitchen

4.-We really need a bigger home at the moment, but dont know if thats possible with the current financial situation seeing that we currently are in a home. Is there a way to get into another home, with the stipulation of selling this one?

Any help is much appreciated, please be easy on us. Im hoping to find a few answers/tips to making this happen before i talk to someone directly involved in our finances as to not be completely blind to the situation to be sold a "pipe dream". I dont want to regret the steps we are currently taking for our family later down the road.

So refinance should be the best route? How bad is it on your credit to apply for refinance at multiple places? My wife works at a bank, and I just opened a new account at a federal credit union. I think the credit union has better advertised rates...

Well, she is my wife not my girlfriend....
She has very stable work history (and pretty good credit for that matter, and she works at a bank). Mine is rolling around on 2 years, but I will also be doing a job change here very shortly.
True on the market change- but we are also worried that its a double edged sword. That our home will increase in value, but so will every other home around. She has a meeting with the "mortgage" group at her job, as the ladies there said there would be no problem to ge her refinanced. But I also want to check the rates at our other bank also. Its a credit union and they are "advertising" better rates that her current job (as to where we also have another bank account). We are working on calling all the credit card companies and placing both of our names on them as to help with my credit....
Thanks for the link, I will also check that out too!