Would it be safe for me to have a temporary crown for 2 months?

No. Temporary crown are put on so you can wait for your crown usually the average time is 2 weeks usually with temporary crown the seal is not great have it finalized.
Depends. How well is the temporary crown was made. Also if the tooth was treated endodonticly or not. I suggest to go back to your dentist and have them finish the work by placing the permanent crown.
Temps. Unless they are long term temps, two-three weeks is a typical time frame. You need to make sure no leakage or recurrent decay occurs. Also if the temp is damaged, the underlying tooth can be affected, or if the temp losses material it can allow movement of the tooth or adjacent teeth, so if the restoration has been made, it may not fit. Get the final done or delivered asap, before it's too late.
Perhaps. Temporary caps are just that, temporary. The sooner they can be replaced with a "permanent" (average life span of a crown 8-10 years) crown, the better. Please don't wait too long.
Not ideal. Well made, well fitted and well cemented temporary crowns can last that amount of time without problems. However, there is no guaranteed of that. The longer a temporary crown is left, the more risk. I'm not sure why you are asking. That question is best answered by your own dentist who is responsible for your treatment plan and care. If that is your choice, get something permanent asap.
Teeth. That's is a long time with a temp. The turnaround on fabrication of a crown is usually about two weeks.