GSM door entry, gate entry or intercom comes up with loads of hits on Google here in the UK.

Get a nixplay from their local Amazon shipped direct. You can then load the images from your end.

We have a Nuki, and use a lock from Yale which is designed for their own smart locks, but works fine with the Nuki. It has its own key from the outside, so doesn’t look out of place at all.

The other option is to get a lock that can leave the key in and still use it from outside. Astral is one brand I think, but when I found the Yale it was perfect.

You need boiler control if that is what supplies the heat if you want to save money.

Given your requirements, an off the shelf solution would probably be better. Evohome is what I would recommend. I have had it for over seven years and it just works. App control of you want, but I don’t touch mine other than to turn it on in November and off in April.

You can get a controller for each room, which will also double up as a thermostat for the room, telling the coordinator to call for heat.