Can I contribute to my company's 403b Roth IRA even thou my AGI is over the limit ($139K) for a personal Roth IRA? Does the fact that it's company managed make a diff?

Yes probably,  a 403(b) plan is NOT and IRA and the IRA rules do not apply to it.    Check with the 403 plan administrator for the contribution  rules to that plan which are totally different form an IRA.

Yes, if the company offers a Roth option.  It is a designated Roth option within the 403(b) or 401(k) and it is subject to the rules for a 403(b) or 401(k).  It is not an IRA, and not run under the same rules as an IRA. 

thank you, that answers my question.