As others have said, don't use anything. You do not have the foundation in training knowledge, experience, or likely strength and starting build to merit taking steroids. Further, and this is just my opinion, drop the trainer. For a professional to tell an average joe in your case to jump on gear just to build muscle to help you lose weight better on his training/diet plan is shady, pathetic (on his part) and downright criminal. This shows that he has no concern for you, but wants you in the best possible physique to use you as a sales pitch to future clients.
I say drop him because even if you decide not to juice, he will either flake, or start throwing equally shitty and unhealthy training and eating plans at you to try and gain the desired effects. With a mentality like his, even if he is just ignorant and misguided in his logic, he should have his certs revoked, he has no business caring for the health and improvements of clients.
On to your specific questions:
1. Most gains that you make after your first cycle will leave eventually. Even seasoned lifters are usually very lucky to maintain even half the muscle mass they built with gear when they are totally off it.
2. Yes, if your diet is in a deficit, just like anything else. You cannot outlift, outcardio, outjuice, etc. a bad diet. If you eat 1000kcal over maintanance daily, then no amount of steroids or fat burners will fix it.
3. Juicing is typically not ideal for losing weight, it is predominately for preserving muscle tissue and strength while using a diet and other substances like clenbuterol or something to cut weight.
All in all, my opinion is do not touch them. From what i read you don't seem to want to jump on because you plateaued with years of good lifting and dieting, nor with aspirations of competing in a strength or aesthetic sport. You are contemplating injecting something into your body that could seriously harm you all because your trainer wants you leaner to be his poster boy.
Also, before he tries convincing you that it's all safe and he has you covered, he is either a dumbass for suggesting them to a regular client on a whim, or highly unethical. That said, it is safe to assume he is either A. too stupid to know how to properly help you with your cycle and pct (given his stupidity in suggesting this). Or B. he simply wont care, he'll supply you with a means of getting gear, tell you to inject and then he'll let whatever happens to you be your own problem.