AbidingOhmsLaw

You can have a hosted e-mail system with your own domain, many service providers will do this. They would have the storage, archive, etc. on their servers. Access would be a web client, e-mail client of your choice, or a bridge demon. Option 2 is a hosted vertual server, so your self hosting but renting a VM server on a providers data center, they take care of the hardware, power, backup (sometimes depending on service), etc. You would set up your OS and e-mail services.

Membrane keypad would have 2 issues that would prevent it, first the membrane is most likely not heat resistant like flexable PCBs and would melt if you tried to solder to it, second the black traces on the membrane are made of powdered carbon in a binder and would not take the solder or would break apart. You could use a pressure fit to hold the contact of the switch to the traces if you where somehow able to hold the switch in place.

What is your intended use? Are you using it for ambiant lighting like in the link you provided? Or an actual stage wash, gobos, fresnels, spots, etc. Your use case will determine how many lumins your going to need and what the power requirements of the LEDs will need to be. The ones you linked are only 15w (~1000 lumins) and that is most likely with all the LEDs on full producing white light where as a typical 575w halogen for a stage lamp is ~10,000 lumans on full. You should be able to make a DMX control using a ESP32 C3 board, you will need some appropate size MOSFETS, appropriately sized power control/regulation, and of course batteries. If I was going to do this I would use power tool batteries for convenience, you can get adaptors on Amazon for your favorite brand .