Validity of a Tourist L type from the US for an International student in the US with a F-1 US visa

Hi,
I am an International student from Europe, studying in the US, with a F-1 visa. I am planing to go to China in late August for two weeks, but will stay in India for two month before that, and leave for Beijing from Delhi. Can I apply for a Chinese tourist L type in Chicago, before leaving for India, that is still valid when I leave from Delhi? Do I also get a single-entry tourist L type for three month as a non-US citizen?

Thank you so much!
All the best,
Verena