This does suggest HPTA repression from E2 and/or prolactin. Both of those are also thought to have direct negative effects other than via T levels. At your age, there should not be any age relate decline of T. Thus the cause can be something more serious. In this situation, it is best to have an MRI to determine if there is a growth interfering with the pituitary gland. Such a problem can also press on the optic nerves which pass very close to the pituitary gland. Vision disturbances, although quite rare in this situation, are part of the spectrum of symptoms.
When the pituitary gland is not working right, there can be multiple effects. Thyroid levels can be affected and that would be consistent with your your energy levels and fat loss issues [which can also be from low T and adverse T:E ratio]. You need to have thyroid levels checked. If you have low[er] thyroid levels, you would also expect to feel inappropriately cold at times. You should read about hypothyroidism at Wikipedia. Note that hypothyroidism and hypogonadism have a large number of symptoms in common. Google "hypogonadism wiki". There is a cross action or coupling of stimulus of gonadotrophins and TSH where high TSH output can increase LH/FSH levels, which does not seem to be your problem. Low TSH output might lower LH/FSH. This may not have any bearing on your situation.
If LH levels are elevated and T is low, this suggests that the testes are not able to produce enough T even as the pituitary is commanding more. There can be problems with injury or vascular disorders. You might be aware of your testes becoming smaller or less firm. You should have them examined by a doctor, all the more if LH/FSH levels are normal or elevated.
If LH is low, you can have a trial of hCG to observe T level response to stimulation of the LH receptors.
Your lack of facial hair indicates that you did not have high levels of T/DHT prior to a loss. Some guys are this way and can have strong libido's while not having strong virilization. Such guys do not have much muscle bulk. Adding gyno and fat issues to this mix does not suggest a normal state of affairs.
Elevated prolactin can lower E and lead to gyno. In this case, this can often lead to depression as elevated prolactin reduces dopamine levels. If prolactin was high, one would expect a large impact on libido and the ability to get erections.
FT labs are important as FT can be in worse shape than TT if SHBG levels are up. Low T can increase SHBG and increased E can increase SHBG.
Some drugs, Rx and OCT can mess up ones T&E levels.
Most of your issues seem correctable with hormone level changes. Young men need to look for root causes that involve the testes and/or pituitary.
It would be good to also test DHEA-S levels. At your age, DHEA levels should be quite high.
With men, young and old, low T levels can cause elevate or high cholesterol levels. TRT often normalizes cholesterol levels. Cholesterol problems are thus a symptom of sex hormone problems. You need to have cholesterol levels checked. The results need to be evaluated in the context of a young normal male, not simply declared "normal".
Arimidex and or cabergoline can reduce E and prolactin, if needed, to remove repressive pressures on the HPTA. While this may be helpful, it will not lead to high T levels and increased/major virilization. It might make you a better low T type of guy, perhaps restoring you to a pre gyno guy without fat problems if you used to be that way once. If your problem is low LH and your youthful testes are LH responsive, hCG injections might provide good results without resorting to T injections. There might be a ongoing need for Arimidex to achieve optimal E levels. E2=22pg/ml is a good target. There are cases where T is low and E is also low. When that happens, lowering E is not going to an option. The testes do produce E and have a fair amount of aromatase. The intratesticular testosterone levels [ITT] can be up to 80 times higher than serum levels; which drive a locally high aromatization rate. hCG injections thus can trigger such a response and hCG therapy might lead to a need for Arimidex.
I have had a fair number of guys in your age situation with such problems. It seems that the HPTA is for some, easily disrupted. I do not see that this is something that is easily fixed. Shifts in HPTA actions at this age often seem to be permanent. This can happen to young men who are low and high virilization types. For low virilization types, the outcomes may be more successful as their bodies are used to performing well on lower T levels and restoration to lower range T levels may provide a good quality of life.
For young men, if TRT is needed, hCG is non optional. If your doc thinks otherwise, you need to find a new doc. TRT without hCG leads to organ failure - the testes atrophy and become non functional.
For lower T guys, the adverse effects of elevated E levels can be expected to be more adverse than the same E levels in guys with higher T levels. E2 control is more important for low T types. In some situations, Arimidex/anastrozole mono therapy may be needed for a better quality of life and a higher life expectancy.
Guys who are low T types, low virilization, who go on TRT and get high normal T levels can expect to have increased virilization, increase facial and body hair. With E control, fat loss often results. Sex drive can increase. Transient sex drive is often very high. Long term sex drive does normalize. E control is essential for long term libido. Serum E2=22pg/ml seems to be optimal for libido and ones sense of well being.
A message for young guys wanting to take a promones or inject with no idea about cycles and PCT: I have seen lives ruined from single events messing with this crap. Again, it seems like there is an age where the HPTA is easily broken. When some young guys do gear, the accompanying HPTA shutdown can be significantly permanent. Some of the "post ban" promones seem to be particularly dangerous, as well as been ineffective as anabolic steroids. Note that drugs to reduce DHT, used to reduce hair loss, can cause permanent damage for some. Young guys should never use those drugs. Note that reduction in DHT is dangerous and that DHT is essential for libido.