Question about Closing for Mortgage Refi

So, I’m closing on a refi in a couple days and just got the numbers. Please help me to understand. I’m going to call my loan officer, but wanted to run it by you geniuses first.
Basically, my closing costs, or amount I’m paying at closing consists of:
1. Cost to pay off current loan ($100K)
2. Settlement Charge, or crap associated with closing (fees, escrow, interest for remainder of month, etc), $2K
These two are added, totaling $102K.
My loan is for $99K.
SO I’m paying $3K, the difference of $102 and $99K.
1). It seems odd that I’d pay more at closing if my load was for less money, but maybe I’m missing something.
2) What is the reason you pay and entire month of interest when paying off loan? Is it because you skipped the first month at the beginning of loan?

Thanks

Also, would there be any reason to anticipate not receiving my current Escrow money back?