I have a question regarding “manual” modeling, i.e. moving and fusing points, extruding and knitting polygons, splitting edges etc.
Right now I perform all these operations like I would in other applications. And the node stack in my SOP window is getting extremely big. Every time I fuse two points I get a new node.

So I'm wondering, am I doing this correctly or is there a better way? If I know that I won't have to go back and change anything, can I “bake” all old nodes into raw geometry, thus lightening the number of nodes? Or should I collapse them into subnets?

And one more question: I am working off of an imported FBX file. Am I right in thinking that if the FBX file gets deleted, the Houdini file won't work anymore? Or does the information from the FBX file get stored within the Houdini file?

https://www.sidefx.com/docs/houdini13.0/model/lock_nodes [sidefx.com]

See this page on how to delete history and lock nodes. Deleting the history should do the clean up you're looking for. Can't speak to the FBX import though.

FBX animation data gets read in chops then applied to geometry. It's independent to .fbx file.

If you dive inside geometry, will see locked file sop. DO NOT UNLOCK that otherwise you'll loose your geometry and you definitely need fbx file.
To be safer side just write out it as .bgeo if you don't not have crazy amount of nodes inside fbx.

Alright, excellent. Thank you both for the help!