The best way to quit a company?

Hey there guys I just wanted some insite.. Pretty much I'm starting off my career with a mega company and after my training OTR with my trainer I have to go back home so I'll be leaving the company . In addition I had signed a contract where they would pay for my school if I stay with them for a number of time.

1) With that said I was wondering if I should I add that company in my resume as experience even if it's for a month.

2) Also can I still work for another company even though I breached the contract?


Thanks

-Blessings to all and your family be safe out there on the road