You have to understand how a VPN works!
A VPN creates a private connection from one location to another. When using a VPN service you are not creating a private connection from one end to the other!. Instead, you are creating a private link from your device (or network) to an intermediate location, and from there onwards, your requests are in the open again. So using a VPN can help to hide YOUR identity and YOUR location. Note that it is only a help in preventing you from "casual" spying. If you were under investigation or serious surveillance then your data would still not be secure!
VPNs work far better when they are used for end to end connections. In those situations, you can still see the source and the destination, but the data is secure from end to end!
your question is based on faith in the government following the law
for what it is worth ,, but the "government" has individuals in it who will do as they feel privileged to do so.. within in the law or not ... it happens all the time they break the law and so few go to prison for it
it happens to lots of people YET until it happens to you ,, you will most often feel they must be guilty ... child support and CPS are big abusers and IRAs as well often uses margins in the law and confusion for subversion
the government can't "see" anything without a warrant. but they record it all...
Probably. Most VPN servers have some record of operation. Sometimes it is complete. Sometimes it is only time of access, not what. And a very few claim no logs kept. But it is very hard to be completely trace-free. Digital activity fingerprints are everywhere, and might be recalled through completely obscure paths and techniques. Few are expert enough to do the deep stuff. Perhaps governments have hired or cultivated them.
Depends on a couple of factors:
1) Can they decrypt the VPN packets. Most likely they can, but that uses a lot of resources.
2) Do they have access to the VPN server? In many countries, government can go in and sieze their logs, showing customers and what they accessed. However, this is usually on a court order, and is a one-of thing. They cannot monitor you live...
3) If they really want, they can seize your computer, do a forensic scan and find out all your browsing and download history (and look at all your files). Again, this would require some court order/warrant to do so.