125ccm legal tune + some questions

Hello, I’m new here and I hardly know myself at 125 and have a few questions. First a bit of pre-discussion: I made my driver’s license (Class A1) this year and bought me a 50cc scooter. However, this one was broken after 2 months and is just standing around since then. Then I had bought a 125er, which is now also standing here. The 125er is a Kinroad “Wind Hunter”. I already know that this is a sogenan It has 4.5kw and 6500 revolutions and has a top speed of 70km/h. For the purchase there were also some tuning parts, which bring the machine to 110Km/h. This brings me to the first question: Can I legally install the parts at all or does something against it? The machine had no TÜV since 2011 and the examination also has to be done. I know that the TÜV costs approx. 55€. But what do I have to do after I was at the TÜV? And w I would like to thank you in advance for all your help.