1. Don't get over 300 psi : this will not harm the marker, but it will harm the gauge, so it will not show good pressure again. Best pressure for the VS2 is around 250 psi, whatever the manual says.
2. Even if the marker is shut down, it drains the battery. With the facts that it takes at least 3 full charged to get the battery fully fonctionnal, it is not anormal that the battery died after 3 days. When full charged, the marker will shoot about 2500-3000 shots in a day, but remember that the battery is drained even if the marker is shut down.
I don't think the heat could harm the battery, actually it's heating up when charging...
3. The stock barrel is OK, and you shouldn't have to think at this right now. Keep your money to get a very good mask, or more paint to shoot
4. There's no way to verify if the velocity adjuster is in a good position. When the marker will be set at 250 PSI, you turn the velocity adjuster to shoot faster or slower. You should use a chrono to know how fast you shoot.
5. check in my sig : there's alot of good information about the Vs2.
Play safe and have fun.