Welcome! I've moved this to "projects" so you can get individualized responses based on your own needs and preferences.
First, we'll need to know a little bit more about what the set up is like. Smartthings is a cloud-based system, which means if the Internet is down or even if the SmartThings cloud is not available, The system cannot send notifications. It doesn't have a cellular option. So the first question is whether that's going to meet your needs for a second home location. A cloud-based system is fine for some people, but it's not a good match for a location where Internet connection is spotty. Or if you need to get alerts when the power is off.
As far as replacing the smoke alarms, you probably won't need to do that. One popular option is to get a Wi-Fi connected acoustic sensor which can hear when the smoke alarms go off. (In the US, residential smoke alarms manufactured in the last 15 years or so all use the same beep pattern.) then it sends you a message that it heard the alarms. It can also distinguish between a water leak alarm and a smoke alarm so send you a different message depending on what is going on.
I have the Leeo acoustic sensor and like it a lot. It typically costs $50, but sometimes goes on sale for $35 or so. We only need one to cover our whole house, but it's a single floor home. You might need one for each floor, you just have to test that. But basically it just has to be within hearing range of your alarms.
The Leeo itself can send you an alert when the temperature goes outside of your desired range, so that's good. But it only works when your power is on because it's a plug-in device, so it may not meet all of your use cases.
Integration with SmartThings is through the free IFTTT service. The Leeo does require Internet availability, but so does smartthings if you want to get notifications. Also know that you don't need to have smartthings at all to use the Leeo, so if all you want is to get notifications when the temperature falls or your smoke alarms go off or a leak alarm goes off, you can get the $50 Leo, a couple of $4 leak detectors, and use your existing smoke detectors and you'll be all set. Again, with the understanding that the Leeo can only send you messages if your Wi-Fi and power are working at the Leeo's location.
There are lots of other options for the various other things you asked about, but I just wanted to mention that one upfront.
In addition, you might take a look at the project reports on the quick browse list in the community created wiki. The "get started" list has a lot of introductory information, although you might not want to start going through that until you have more of an idea of what you're going to try to do. There's a lot of information there.
There's also a "second homes" list which might have some topics of interest, including discussions of remote management and handling alerts from multiple locations.