Sounds like you've got a lot of learning ahead of you. Most here would recommend that you do all the maintenance before hand. Make sure the valves are adjusted, carbs completely stripped and dipped, change all your fluids and verify the electrical/charging system is working properly. NEVER depend on the PO's information to be accurate. There sole purpose is the dump their abandoned project on any unsuspecting victim. Most here would advocate getting it running right in stock trim before starting on the modifications. It's much more predictable and straight forward when trying to troubleshoot issues. From reading your posts it seems like the petcock is probably shot. Don't try to rebuild it. The success rate is very poor and, in most cases, the stock replacement is still available.
Don't try to run the bike till you've done the basic maintenance or you risk much damage. These bike will be very dependable as long as you do what's needed. One of the big problems encountered is a lack of valve adjustment. The bikes tend to tighten the valve gap over time. If not checked and adjusted, the result will be burnt valves and a major tare down. The second biggest issue with these bikes is electrical system related. The charging system depends on a functioning stator and Rectifier/Regulator. R/R for short. If you modify the electrical system and make the lighting system "more efficient", you WILL destroy the stator or the R/R unless you change the R/R for a series unit first. One of the many reasons we usually recommend starting stock and them modding.
Don't try to run the bike till you've done the basic maintenance or you risk much damage. These bike will be very dependable as long as you do what's needed. One of the big problems encountered is a lack of valve adjustment. The bikes tend to tighten the valve gap over time. If not checked and adjusted, the result will be burnt valves and a major tare down. The second biggest issue with these bikes is electrical system related. The charging system depends on a functioning stator and Rectifier/Regulator. R/R for short. If you modify the electrical system and make the lighting system "more efficient", you WILL destroy the stator or the R/R unless you change the R/R for a series unit first. One of the many reasons we usually recommend starting stock and them modding.