With old software, you are exposed to threats because all the weaknesses are well-known, and the “security holes” are no longer getting plugged by updates.
So be careful of the web sites you visit, those unexpected emails that invite you to “update your bank details” or whatever. Don’t download new apps (if any are compatible 
) unless you’re sure of the source, etc. It’s really difficult to say where the dangers might lie exactly.
<joke>Of course, there will come a time when even the malicious software is no longer compatible. When you get to that stage you’re in the clear. I mean, who writes viruses for MS-DOS these days? </joke>
As to the replacement battery, you might get in touch with a good, reliable repair shop. There may be solutions using batteries that have compatible contacts and voltages but are smaller than the original. In that case padding can be provided to keep the battery in place.
Fairphone official support may be able to suggest replacement battery types.
Seriously, I admire your desire to “keep that old gem going”!