Would going on rollercoasters effect my hair transplant at all?

It is best to contact your doctor about post operative care and instructions since each doctor has a different regimen.In general PRP or micro-needling is not a normal post operative regimen.

Finasteride can cause low libido. It can also cause low mood and anxiety. Combined can cause erectile dysfunction.

It is normal to shed transplanted hairs weeks after surgery.  The new hairs may take 6 to 12 months to grow.  If you see spaces, there may have been no hairs placed there or the hairs may have fallen out.

You are having donor shock secondary to a tight closure after FUT. Hopefully most of it will regrow over the next few months. If not, your options include SMP, FUE, or scars removal with a balloon expander, Dr. Robert Jones

With this amount of time that has elapsed since your hair transplant, there is no issue with wearing a cap as you described.  Contrary to popular belief, wearing a hat does not cause baldness and in your case, the cap will not affect your hair transplant.

There are side effects with any medication.  Most common side effect of propecia is sexual or erection problems which occur in 1 to 2 % of the time. You should discuss your concerns with your doctor who prescribed you the medication.