No. Can not break. Depending on length of strings, and uterine size, they can retract up inside the uterus.
Unlikely, possible. The strings have not been known to break off but depending on how short they were cut and how large the uterine cavity, they can retract up inside and not be felt or seen. Cramps may happen especially early, if it has been in for a while and strings not felt and new cramps, an evaluation is warrented to make sure it's not in the uterine wall.
I've had my mirena (levonorgestrel) for 2 years, am still able to feel the threads when I check. I had intercourse 7 days ago and he pulled out. Should I be concerned?
I don't see why. Since you are using one of the most effective methods of contraception and you can "feel the threads", your risk of pregnancy is really quite low (less than 1%). If you and your sex partner do not have any sexually transmissible infection, your risk of a pelvic infection are also quite remote. If you need to be reassured, consult a Gyn to be screened and ask your man to use condoms.