Are there readily available accomodations on these trekking routes or do most people carry a tent.
Yes. They can be crowded in March, April, October, and November though.
Are there areas to re supply or do you need to bring all resources for a 10 to 14 day trip
There are plenty of places to resupply.
Are there any mountains to attempt to summit in the area?
Yes, there are mountains of all levels of difficulty there.
Here is a partial list of peaks that can be climbed with only trekking skills and with no extra equipment:
https://www.summitpost.org/nepal-trek-a ... ins/955631
Here is a list of the "trekking peaks", some of which are easy technical peaks. Some are quite hard though. They have a large range in difficulty.
https://www.summitpost.org/nepalese-tre ... aks/171056