Does new hair come out after 6 to 7 month of FUE HT in crown area? How long can we take finasteride 1mg tablets for?

It can take 6 to 12 months after surgery to see results.  If you are concerned it is best to contact your doctor.It is also best to discuss medication with your doctor who can oversee your treatment plan to meet your goals.

At 5 months you still have a ways to go in terms of hair growth. I wouldn't worry about the results you're seeing so far simply because some people grow a lot in the later months, leading up to the final product after about a year. And if you don't have side effects from Finasteride now it's doubtful you'll develop any. But if you feel you might be having some contact your doctor.

Transplanted hairs start to visibly regrow between months 4-6. At month 6-9, you may  expect to see growth for  80% of the transplants. Again, due to the random cycle of hair growth, not all grafts will start growing at the same time. Initially, the hair my be thinner and finer. It will gain length and density as it matures. Full growth from the transplants is usually achieved at 12 months.  I usually recommend  my patients to use  finasteride for one year . Better to take it  after meal .

If you have been taking finasteride for 5 months without any side effects you will not likely ever develop any.  As far as new hair growth, you can expect more growth.  At 6 months there is only about 50% of the new hair growth.  You can expect the full outcome 9-12 months.

Hair after a transplant takes 8 months for 80% of the growth to be evident and at least 1 inch long by then