About to list my primary residence, please offer advice

[Robert Hastings]

i hope to list my primary house before the end of the month.  we are doing last minute repairs before we stage and list.  i have an appointment with our accountant in a week to file taxes so we can submit our return to our lender so we can work our final numbers.   we have a combined income of close to 220k.  plan on putting over 20% down with a large amount of reserves.  i plan to keep my debt to income around 45%.  

whats the difference between interest rate and APR? what percentage will my monthly payment be based upon? a mortgage of 100k for 30 years with a "rate" of 4.0 is $477/month (Google mortgage calculator)...will that be my monthly payment or will it be adjusted because my APR will be slightly different?

if we are able to secure our mortgage and one or two years later, we our credit gets a bump and my wife and myself have A+ credit, can we refi for a cheaper monthly payment?  right now my credit is close to 790 but my wife is hovering around 620.  

i need to sell my home in order to buy.  it sucks but i cant avoid that contingency.  should i wait until my house is under contract before i start placing offers?  or, can i wait until i get my pre approval letter/proof of mortgage approval?  i know sellers dont like offers with a contingency but i feel like our offer will be solid enough to stick. 

ideally i would like to close on selling my house and buying my next house same day or as close as possible.  

any input would be appreciated!!