I'm currently using foobar v0.9.3.1 and whenever converting from FLAC to mp3 is fine, but when I change some tags in the mp3 (such as album name) Audio Identifier shows the 'encoder' as FhG (sometimes) or nothing would appear under encoding options. Again, this only happens after I edit the tags, before that, Audio Identifier reads it correctly... LAME 3.97 and V0 under encoding options.

Maybe your problem is related to foobar using ID3v2.4 tags. I don't know Audio Identifier, but you could surely check it's ID3v2 compliance. Personally, I don't edit ID3 tags with foobar because of that but use mp3tag instead (there's a lot more options what kind of ID3v2 tags are used).

Well, what I'm doing is, after the FLAC files are converted with foobar, I'm changing some of the tags manually by going into the file properties and the summary tab. So the tags are not touched by foobar, unless you mean I should just tag them with my tagging program and not by going into properties.