Hi, first let me say congratulations for making the step to start gymnastics. 16 is in fact a great age to take up the sport. You have many advantages, you are probably finished growing or just about finished growing. As young kids grow they constantly have to rebuild their strength, redevelop their flexibility and change the way they do skills. This is especially hard if they are going through a major growth spurt. Secondly you may not be as flexible as your younger counterparts but you will build strength more easily. Thirdly you are there for you, because you want to be and not because your parents put you there, you will have the dedication and drive from that. Also it can be a lot easier to learn things from your coach as you have a deeper understanding.
Most people do start gym younger because it takes many, many years of hard work to reach an international level, for the aim of reaching their peak skill when they are your age and little older. This means that you will probably not reach your peak skill until your late 20's so it may be a little late for you to go to the olympics. But who cares, there is a lot more to gymnastics than that. I hope you continue to enjoy the sport through out the teen years through to adulthood and beyond.
I don't reccomend that you stick the stick it beam to your tramp. If you want to practise more advanced skills on your tramp draw a line down the middle. Be careful only to practise those skills which you are confident with and can do easily at the gym with no spot.
For working vault, try using the actual vault table for the level 4 handspring to flat back vault. Stack mats up on the landing side of the vault up to the same height as the vaulting table and do the handspring flat back vault on there.