You asked a couple questions:
What kind of data can a VPN server log or monitor?
Date, time, which server you connected to (IP and port), the size of the request, the response size, how many times you connected to it.
Can the VPN service provider monitor or intercept the full length of the transmitted data, or are they able to do so for some part of it?
It depends. If the connection is encrypted (TLS, SSH, for example), the provider can intercept the message but cannot know its contents, as the encryption is meant to protect exactly against this kind of attack. If the connection is not encripted (FTP, Telnet, HTTP, POP3, and others) they can monitor and intercept everything.
Not only monitor, but copy, alter, and replay any message. Logged into a plain FTP Server? Your credentials can be copied. The files you transmitted can be copied or changed.
Also, can they alter and re-transmit the data as it passes through the VPN server?
Same as above.
How do I know that the provider isn't doing such thing?
The Terms and Conditions. Yes, that boring page full of legalese that almost nobody reads. Usually they will tell there (in cryptic language) what they monitor and what they don't.
Will they monitor you? Probably. Like every single Facebook beacon, every Google Analytics script, everything on everywhere you navigate. It's bad? Not worse than everything around you. And that's a legal thing to do (unless they say they will not monitor).
Will they steal your credentials and your data? Unlikely. Besides being illegal on almost every jurisdiction, it would bury their business pretty fast. They have other means to make money, and stealing data from their customers isn't the best one.
How to be sure you are not being monitored instead of protected? Rent your own VPS and install your own VPN. It may seem complicated (and it's not simple), but with the correct tutorial you can have a Linux installed and running wireguard in an afternoon, for less than 5 dollars a month.