1)Is there a set fee for sweeping or is there a way to find out how much the fee would be to sweep? I know you can adjust the transaction fees, but that did not seem to do anything for sweeping.
There is no set fee. You can choose your fee.
2)12.7kb is large, looking up average current fee is 450 satoshis/byte using that it would be about .057BTC ~ $240 fee to sweep in a little over 1BTC. Is there a better route to get the coins out of multibit and into the trezor?
You can set the fee to about 200 satoshis/byte, and the transaction would go through in about a day. Also, consider getting rid of the inputs that contain dust amounts of btc to reduce the transaction size.
3)My balance on my Multibit classic is just over 1.04BTC when sweeping the keys it says amount received is 999.9 mBTC. Is that how much would show up in electrum after the fees or do I need to check for unconfirmed transfers? which the last transfer was in 2014.
Can you give us the transaction?