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
)