Yes, OBS can Record and/or Stream. So, Record only is no problem
Getting remote site input is NOT a native capability of OBS. IT is a tool for compositing local sources.
There are plugins and other tools to get remote content into OBS. What you need to ask yourself is: are you the type of person that prefers free and is willing to put the time into learning how to use a specific tool? or would you rather pay, have nice manuals, support desk, etc? The answer to that will help point you in the direction most appropriate for you
Though not free, probably a more mature supported option, would be NDI Bridge (I think it is called). Even with that though, when combined with OBS, you will have some tech learning you'll need to do to reliably operate such a setup. There are options like obs.ninja that may suffice. I'd recommend searchign this forum for discussions and figure out what most closely resembles your use case
