Been a while since I was in that area, but in general:
1) Are there reports of luggage theft or even pickpoketing aboard the flexibus?
I am sure there are some, maybe not, but that could be said of any transport in Italy. I assume you mean Flixbus, they are fine in general, but there are other buses such as Itabus.
2) Do the taxis at Marco Polo airport taxi stands go to the Trieste cruise port?
If you find one willing, sure, but for that distance, best to set up something ahead.
3) Are there taxi stands at Piazzale Roma with taxis that go directly to the Trieste cruise port? How much would it cost?
Same as above. As for cost, I have seen estimates of 200 euro or more.
Not sure exactly where you will be starting from, are you just arriving at the airport and going to Trieste? or are you staying in Venice then need to get to Trieste?
An option you have not considered is train, from Venice SMN, the train takes 2-3 hours and costs 20-30 euro, from Trieste station you can get a taxi to the port.
There may be shuttles dedicated to runs to the port from Piazzale Roma in Venice, you might ask your hotel for suggestions, or maybe others on here have thoughts.