Can I set my father's phone to auto-answer my phone calls? Is there a phone app that allows me to listen in/see him so I can monitor him?

Joniker: Adjust the ringtone on his phone to be loud and a version such as a dog bark that he would be more apt to hear. If he requires help by way of the Lifeline being activated and he doesn't give a verbal command, I believe EMS responds.

If it's an iphone you can set up the haptics so that the fashlight flashes when there's an incoming call. Not sure if that's available on non-ios platforms, but might be worth looking for under any accessibility settings.

I would get a camera and install it he usually sits plus put one in his bedroom to check on him at night. Even if you could set phone to auto answer, you might hear TV but unlikely he'd be able to hear you with it up so loud. Just hearing the tc blaring won't give you any assurance that he's ok. With camera, you can peek in on him if he doesn't answer phone and see that he's ok.

They have Amazon echo screens for two way visual conversations, but he would have to hear it, just like a phone, and answer for you to see him. Another thought would be a phone for hearing impaired. Some can be set up to make a light flash when it rings. He might not hear the phone ring but possibly see the light flashing off/on. Check his local phone company for phones available to him for hearing impaired

Iphone has the ability to auto answer. I got mom a standup charger and zip tied her phone to it so she would not lose the phone or forget to charge it. I deleted all phone numbers that I didn’t want her to get calls from and in setting I selected only allow calls from contact list. This allows her to get calls but not scammers or robo calls. The most important thing to remember is to hang up on your end. It has been wonderful and sometimes more reliable than my alexa echo which uses wifi. I have both. It is peace of mind along with blink motion detector camera ( i told mom they were speakers). I set her auto answer to 10 seconds and put an obnoxious Duck Quacking sound. It gets her attention!

I found an article that you or others or others following this subject might find of interest.
https://aginginplace.org/medical-alert-systems/monitoring-system-for-elderly-in-the-home/

I think Apple has a watch with useful tools.

https://www.apple.com/watch/why-apple-watch/

We have used a combo of an Echo Show and a security camera to communicate with and keep track of my mom. She also doesn’t hear well and often didn’t hear her phone even when she could figure out how to answer it. The Echo Show makes a sound she is able to hear even over the tv plus she can see us and we can see her making conversations much easier. We also have a security camera over her medicine table that also enables us to see if she is in the room and ok or not without intruding on her privacy too much. Her need to have the tv blasting, especially when she wasn’t able to mute or pause it consistently, was a real issue too so we hooked up a splitter thing that allows us to have an ear bud (or two she just doesn’t use one) plugged in which she prefers anyway to listen with and mute the tv in the room.

I believe the RAZ memory cell phone has an auto answer setting. You, as the caregiver, control the phone through the caregiver portal and can choose the auto answer feature.

Like in the cheesy commercial
"HELP, I've fallen and I can't GET UP.
Guess it works unless the person is not unconscious

Google information on Echo Show to see if that might meet your needs. There may be other devices that are similar.

There are many security cameras that allow you to check in from your phone. Nanny cams are also accessible by phone.

If your dad is hard of hearing, you can get a flashing light for his phone so he can see when it's ringing. Most iPhones have this setting, so just Google how to activate it if you go that route.

I have a Samsung and it allows answering automatically but only when a headset or bluetooth is being used.

I know you didn't ask, but what's the lifeline button for?
Maybe get a security camera that you can monitor from your cell phone or computer.

People have posted that they use Alexa this way, it might be worth checking into.