I have heard that after Eid-ul-Fitr Saudi Embassy does not give Umrah Visa uptil the Hajj period. Is that true ?
Also to prove that the person accompanying you is your mahram ..should the proof document be given along with visa application at the time of its submission.
or you just need to keep the proof-document with you at all times when you finally leave for Umrah.
I have heard that after Eid-ul-Fitr Saudi Embassy does not give Umrah Visa uptil the Hajj period. Is that true ?
Yes that is true.
Also to prove that the person accompanying you is your mahram ..should the proof document be given along with visa application at the time of its submission.
or you just need to keep the proof-document with you at all times when you finally leave for Umrah.
I'm not too sure about that. I think it depends on which country you are applying from and which country you are a citizen of. In the Pakistani passport for example, the name of the father (for unmarried ladies) or the name of the husband (for married ones) is mentioned. Therefore you don't need any additional proof, if your father/husband is the Mehram traveling with you. However if no Mehram is mentioned in your passport, then I think you need to submit a proof-document with the visa application. If you intend to travel with your son for example, that would be a birth certificate listing you as his mother.
What's the longest amount you can stay if in transit (to/from) U.S.? What if I just wanted a stopover for general pilgrimage, and other sightseeing?
You can get a transit visa from the Saudi Embassy in Washington DC, that would entitle you to stay in the Jeddah/Mecca area for up to 72 hours. It does not allow you to travel to Madina though.