Purvanchal Express - Poorvottar ka Sikandar

I have to visit Mumbai for 1 day business trip, arriving LTT by 18030 at 4:50 hrs. I have some queries:
1. How is the connectivity from LTT to MMRDA Exhibition Center, Bandra Kurla Complex? What is the fare in general for auto/taxi?
2. Cloakroom facility available at LTT? If yes, which platform?
3. How is LTT in general, I mean safety, ambiance...
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@ 4:50 in morning? Any dormitory available for quick fresh-up? Any good food outlet for breakfast?
PS: I'm not opting for any hotel or lodge as I have to stay in the city for 4-5 hrs only after that I have to continue my onward journey. Inputs from local members are appreciated. Thanks!