I live in Canada where it often gets below -20c in the winter. I have a cheap electric water heater (eco smart) and it does our house of two people fine. It’s a little slow to fill our tub, though. Cold weather has nothing to do with tankless vs storage water heaters. The company we hire to do our plumbing and HVAC installs in new homes we build often recommends Navien gas water heaters. They work great at high flow rates but require direct ventilation of the combustion gas. The last two homes I built used Navien tankless heaters and the home owners are extremely happy with them. Talk to a different installer in your area. HVAC contractors are probably to be the most knowledgeable.
The one 2x4 that’s notched might be connected to the other webs that form the truss? If that’s the case I wouldn’t be removing that one. It’s hard to say what the red one is doing, is it directly below a roof joist that makes up part of that flat roof section? You could pull it out (the building won’t fall down) run another plate on the top about 30" long and add two new boards 24" apart and that would be sufficient.