Schengen visa questions

[imi_user08]

I'm a citizen of India and GC holder. I am going to apply for Schengen visa at German consulate in Los Angeles. From their website, they require a proof of medical insurance with coverage of at least $37500. I've medical insurance from UHC thru my employer. UHC rep said that they cover medical emergencies outside of US and will be sending a letter stating my coverage limits including out-of-network coverages.
Is there any need to buy additional insurance? Has anyone experienced any visa rejection due to lack of additional medical coverage?
I'm going to carry following docs when I appear in person:
- Original GC, Passport
- Employment verification letter
- Bank statements
- Letter from UHC for medical coverage
- Printout of E-ticket showing itinerary
- Letter from escorted tour company who is arranging my hotel stay.

Is there anything I am missing?

I'm going to apply for multiple entry UK visa as well. Is it possible to get both visas the same day since the German and UK consulates are clsoe by? Or do I have go there on separate days? Do both consulates accept cashier's checks in USD?

Appreciate your feedback.

[Triple Citizen]

I doubt you will be able to get both visas the same day. Most consulates take visa submissions during the morning and successful applicants are given their pasports back during the afternoons.