If your mortgage is owned by Fannie or Freddie look into the HARP program. If not, you can avoid an appraisal with a streamlined refi. Streamlined refi is not eligible for the lowest rates on the market though so it really depends on your exact situation.
Shop around for it. There wont be a negative effect on your credit score for inquiries made within the prior 30 days.
You need the approval of whoever is on the account with you. A joint account means you both have an equal share, so both of you need sign off on it.
You could do a cash in refi to cover any closing costs, but as a general rule if you shave 1 point off your interest rate you will make out big time over the course of the loan even with the added closing costs.