Yes. Your pituitary responds to the increase testosterone in your system by saying "oh, we have enough now, I can stop overmanufacturing LH/FSH". If you didn't see a decrease while your testosterone levels are reasonable (500+), then there's a serious possibility that there's a hormone-producing tumor involved. You're young, so this is unlikely, but it is a possibility.
I'm honestly uncertain. Your TSH levels do not indicate hyper; if they were less than 0.5, that would be something to look into, but 0.88 is a great level to have it at.
Were you using AAS before? For how long? A side effect of AAS use is testicular atrophy; while they will usually recover most of their effectiveness, it is possible for there to be permanent damage caused by AAS. By this, I mean that it is theoretically possible for AAS abuse to cause primary hypogonadism.
There is some concern that finasteride (propecia) can cause irreversible sexual dysfunction, including testicular functional atrophy. It is an unusual side effect, but it is possible - even with only 6 months' use.
You aren't REQUIRED to tell him anything. If he finds out (e.g. he's in the same clinic system as another doctor that you have, and therefore has access to your medical history including tests) then he may drop you as a client because it compromises his ability to trust you as a patient. In some extreme cases, the clinic may drop you as a patient altogether, and even contact your insurance about the incident. This is up to you - some people prefer to keep things from their physicians so that they can advocate for their own health in their own way, others prefer to have their physicians know everything and try to find a physician that will work with them regardless.
Addendum: if you lie to a physician in a manner that would allow you to do or obtain something illegally (e.g. obtaining a testosterone prescription by falsifying lab results), then you ARE responsible, and there may be legal penalties.