In 7 card stud, with 3 of the same suit and only 1 or 0 of you card out, what are the odds of drawing a flush by 7th, also with three connecting cards, what are the odds of drawing a straight by 7th, and starting with 3 of a kinds, what are the odds of losing the hand against 2 opponents by 7th

The answer to three flushes:
3 flush on 3rd street - chance of making a flush by 7th= 23.6% with none of your suit exposed, 19.6% with one of your suit exposed.

Chances of making a straight with 3 connected cards with no gaps is 16.4% with all possible straight cards live.

I am not sure how to answer the third part of your question, as there are times that you start with rolled trips and are already behind (yes, I am still complaining about those rolled up J's beating my 888 )

222 = 89.1% vs. random
333 = 89.96% vs. random
444 = 90.53%
TTT = 92.55%
AAA = 93.31%