CAT s62 pro can't answer my phone when it rings

Sounds like your proximity sensor has died. That's the sensor that tells the phone when you have it up against your ear so it turns off the display and disables the touch screen so you're not butt-dialing with your face. The sensor is only active during a phone call, so it's apparently stuck on; as soon as it's activated it's telling the phone your face is against the phone even though it isn't.

I'll take a look and see if I can locate any repair information on your phone, but yours isn't in high demand so it's possible there won't be much out there.

In the meantime, if you have a case and/or screen protector, try removing those, then clean the screen and see if anything changes.

After some searching, I located a teardown video that shows the location of the proximity sensor inside the case and has enough information to enable you to get to it. Now, this is a teardown video, so they remove a lot more parts than you would need to; it looks to me as though you just have to get the motherboard out and you should be able to replace the sensor. The sensor itself is mentioned at the 6:58 minute mark in the video.

CAT S62 Pro Rugged Smartphone Disassembly Teardown Repair Video Review - YouTube

An online search turned up several vendors including a few on eBay that are selling that part for your phone.

Now keep in mind that should fix your issue with the screen blanking on phone calls, but it's unclear to me exactly what relationship that may or may not have to the problem you're having with your hearing aid app; I'd suggest fixing the proximity sensor first and seeing if the hearing aid app starts working or not.