Various problems with my Vespa Sfera 50 NSL

Hello community, have a few problems with my scooter, I am a trained car mechanic but as for scooters or 2-strokers I am the total Depp, I hope you can help me. Then I start with my problems. 1. My Vespa has problems starting in the early morning, if it is very warm there are usually no problems. 2. If the Vespa is warm then it can be that it runs out in the stand gas. At the start again there are also problems. 3. Furthermore, if it is warm after about 3-4 It feels on a flat track as if the brakes are easily tightened and released again. Irregular 3-6 seconds clock. 4. The battery is now also Platt. Had to charge the battery regularly externally. I measured now and it is at full throttle only approx. 7-8 volts (without light). In my opinion it would have to be min over 12V. Please for information what it could be, since I have no pale glimmer as said by 2 clocks. Thanks in advance.