Ancient ex alarm service guy here, helpful if looking at an ancient intruder alarm . Obviously you’ve sorted it OP.
Yes you can mask PIRs for pets but even 20 years ago when I got the hump with the industry, pet friendly pirs were a very cheap option on proper wired systems.
Yes the sounder ‘should’ stop after 20 mins. If you post a pic of the system I could probably say if it’s worth saving or throwing in the bin. Some of the old systems were pretty bullet proof.
All that said, despite the fact I could fit one for free, I’ve never wanted an alarm on my house.
There is a way of shutting the sounder up from inside, but it’s a bit risky and a big no from a health and safety point of view.