Originally Posted by Seeker

Firstly, I admire your patience, these faults can drive you crazy.

Petrol leak: might be a sticking float valve. I'm never sure how much to say in case you're familiar with how it all works. The bottom of the carb is basically a little petrol reservoir known as the float bowl, petrol is pumped into the bowl until the float which is located within the bowl rises to a set level at which point it shuts off a small valve. These valves can stick which would cause a problem (with leaking fuel) if the engine was running. The curvy has a mechanical fuel pump that requires engine pulses to operate a rubber membrane which pumps the petrol. I don't know whether the pump can leak - IF it can leak and IF the float valve stuck, the float bowl would overflow (but usually down a drain tube under the bike). Whatever, it sounds like the tank and carbs need to come off again. You can get inexpensive carb rebuild kits off ebay which contain new float valves - you can check the valves by blowing into the carb (where the petrol would normally go) and gently raise the float to see if the airflow shuts off. Incidentally, the float level is critical so be gentle with the floats - adjustment of the float level is usually done by bending a tab on the float itself (height spec in manual).
The curvy manual shows how to test the fuel pump and the fuel valve. There are a lot of rubber membranes in the fuel system which may be perished which are causing your problems.

The video that shows you unsuccessfully trying to start the bike - it sounded to me that it was cranking slowly because of a flat battery.