Folks
I have read through all the baggage allowance threads but unable to find a conclusive answer to my current trip. I am booked on united stock ORD-SFO-SIN and MAA-FRA-ORD (open jaw ticket)
ORD-SIN are united operated flights (flying the dreamliner for the first time and United baggage allowance is 2 bags
MAA-FRA is operated by Lufthansa on LH metal and FRA-ORD is on UA metal
My e-ticket states only 1 bag allowed from MAA-ORD for free.

Question: what is my baggage allowance on MAA-FRA-ORD?
1. Since United is the marketing carrier do I get only one checked-in bag for free or does Lufthansa rule of 2 bags apply?
2. US DOT rule examples talk only about round trip. But assuming DOT rules apply the first segment of my flight allows me to check in 2 bags for free (ORD-SIN is 2 bags but MAA-ORD is only 1 bag as per United). Does this allow me to get 2 bags on the return from MAA-ORD?
3. Does the MSC apply (most significant carrier) rule apply with Lufthansa as the MAA-FRA is geographically greater distance than FRA-ORD

Called United airlines and the agent stated that I will get 2 bags as Lufthansa is the operating carrier but he was not exactly sure when I asked him about the DOT ruling indicating the marketing carrier as the dominant one.

what should be my best plan when checking in at MAA?