1. Can she file divorce case while she is still in US ?
It is you who are aggrieved by her continuing adulterous life even after marrying you, so why are you bothered about she filing a divorce case against you, in fact it is you who have to initiate the process from your side to discard her from your life. Well, she can file a divorce case at US if the law permits her to do so for a marriage which hardly lasted for 6 months, but you can always contest the same and denyall her allegations to prove her false especially based on the evidences you possess to prove her adulterous life.
2. If yes what should i do to stop her ?
Yes you can decide to contest and prove her false with the help of merits in your side.
3. what necessary steps i should take to make my position strong as i dont want to give divorce without the actual facts being mentioned on record ?
The documentary evidences in your possession to prove her adulterous life shall make it a strong challenge to her false divorce case and you can bring her character to the lime light, she may try to come for a compromise during which you can dictate terms.
4. How can i force her to come down to india for all the court proceedings ?
Being a US citizen, you cannot force her to come to India even you may try to utilise any law, because she is not a hardcore criminal that you can seek for her extradition. Ignore it if she fails to come to India, you can proceed as per your own action plan on this issue.
5. Does the court recognises evidence like chat history where she is talking about her past relationships with ex's and affairs. also things like screen shots of her chatting with ex asking him out to meet, asking me not to show her past to her parents or any other family members ?
All these things are not admissible as evidences in the Indian courts of law. It is a mere waste of time to establish her adulterous character by producing such evidences as they cannot be considered in the court even to corroborate your statements. Moreover, being a Muslim by religion, you cannot file a divorce case in the court of law, you should settle it as per sharia law by pronouncing talaq before some witness and communicate the same to her properly and to follow the post talaq procedures by offering her the mehr amount and observing iddat formalities.