You asked a few questions:
What kind of data can a VPN server log or monitor?
Date, time, to which server you have connected (IP and port), size of the request, response size, how often you have connected.
Can the VPN service provider monitor or intercept the entire length of the transmitted data or can it do so for part of it?
It depends on whether. If the connection is encrypted (e.g. TLS, SSH), the provider can intercept the message but cannot know its content, since the encryption is intended to protect against this type of attack. If the connection is not encrypted (FTP, Telnet, HTTP, POP3 and others) you can monitor and intercept everything.
Not only can you monitor messages, you can also copy, modify, and play them back. Signed in to a simple FTP server? Your login information can be copied. The files you have transferred can be copied or modified.
Can you also change the data and retransmit it when you go through the VPN server?
The same as above.
How do I know that the provider is not doing this?
The general terms and conditions. Yes, this boring, legalized page that almost no one reads. They usually say (in cryptic language) what they are monitoring and what is not.
Will they monitor you? Probably. Like every single Facebook beacon, every Google Analytics script and everything you navigate. It's bad? No worse than everything around you. And that's a legal thing (unless they say they won't be monitoring).
Will they steal your credentials and data? Unlikely. Aside from being illegal in almost all jurisdictions, it would bury their business fairly quickly. They have other ways to make money, and stealing data from their customers isn't the best.
How can you be sure that you will not be monitored, but protected? Rent your own VPS and install your own VPN. It may seem complicated (and it's not easy), but with the right tutorial, you can install Linux and run Wireguard in one afternoon for less than $ 5 a month.