There are several different ways to do what you are asking about, so I suggest you start a new thread under projects so people can help you with different suggestions and any questions you may have about them. You can put it under projects.
To give you two quick answers:
The ring keypad will work quite well with Smartthings using custom code, but the best custom code for this is behind a paywall in rboys library. You pay a one time fee and get access to the entire library. This is a very popular option for those who are OK with paying third-party fees. You can read more about this in the following thread:
[RELEASE] Ring Alarm Keypad (2nd Gen) Device Handler
As far as triggering Amazon routines from smartthings, that’s very doable by creating a virtual sensor that you can turn on and off. It requires custom code, but nothing you have to pay for. The only thing is this worked great right up until April 2020 when smartthings introduced a new version of their Amazon skill, and ever since then it’s been glitchy. It usually works, but every once in a while it will stop working, sometimes even for a week or two, and while that’s OK for convenience use cases, I’m not sure I’d want to build a security function around it. 
But here’s the community FAQ for how you do that:
FAQ: Can I trigger an Echo Action without Speaking to It?
However, as I mentioned, there are other ways to do all of this as well, so do start your own thread in projects as otherwise we are getting pretty off-topic here.
Oh, we should also say that whatever method you choose as an alternative, you do need to be aware that the old ADT/smartthings dual logo panel could do a lot more things when the Internet was out then anything based on a new smartthings/Aeotec hub can. 
. For example, you can’t even arm/disarm unless the Internet and the smartthings cloud are working. And anything that requires custom code, including the two links I just gave you, would require the Internet. And obviously anything that requires an echo routine. So that’s just something to take into account as you consider alternatives. But that’s another reason why you should start your own thread, so we can discuss all the details.