That is not strictly speaking true. There have been no long term studies for the most recent mRNA vaccines, but mRNA technology has been in development for many years with much of the effort going into studies of human safety. This long period of development and testing is how the method of packaging the mRNA in a precisely engineered blob of fat came about.
Yes, though that might depend on your definitions of both long term and vaccine. There is actually a quite interesting body of literature surrounding these developments, so it might be worth doing some searches and some reading.
If the drug breaks down rapidly in the body, yes, we can indeed know that. Then there can be no mechanism by which it can have long term effects. That's what happens with the delivered mRNA.
But out of interest, what about the people who have long-haul COVID, do we know the mechanism how they experience long term effects from the actual disease.
Would it be possible that vaccines created long-term effects in the same way?
What is the "mechanism" from the vaccine which has caused some people to get thrombocytopenia, bells palsy, temporary deafness, and other such side effects in just the short term?