This is a lot harder than most people think. You should be more realistic in your goals.
Not really. If you did a cycle, it would be a complete waste unless you know how to train and eat. Based on your admission that you you are at least twenty pounds off in your body composition, you probably haven't maxed your gains from training and eating and a cycle would be a waste.
You must know something most other people don't, because adding ten pounds of muscle is very hard.
This is highly unlikely. How much time are we talking? How did you determine how much fat you lost and how much muscle you gained? BIA? Calipers? Dexa Scan?
I understand you probably feel better, and have lost some weight and inches, but this kind of a swing taxes the limits of credibility. I guess it's possible if you were a big fat bastard to begin with, but it's still a stretch.
For the OP, TRT is great, but it's not a magic bullet. A responsible physician will not have you on supraphysiological levels of test, and so weight loss and LBM gain is only going to be as good as someone with normal T levels. Running a cycle will help, if your diet and training are dialed in - otherwise, it's a waste.
I suggest you take a look at some of the contest prep threads to see what those guys did to get rid of fat. @BrickHead and @robstein spent a long time in calorie deficit doing LISS and HIIT workouts to get ripped. I suggest that would be a better alternative than running a cycle.
If you're lucky, you can maybe add five pounds of muscle in a year if you are in a caloric surplus - in my humble opinion. Unless you're a 125 pound teenage boy. Then, all bets are off.
I suspect some of the other more knowledgeable posters would agree with me, and would like to hear from them.