Basement – Should I remove cold cellar wall insulation below grade to allow ground heat to warm the space in winter

You could certainly perforate the lower section of the sump basin with small holes (1/4 inch/6mm or less would be my preference, but some might go twice/3 times as large - depends in part what you are bedding it in)

Outside the basin, you'd want washed stone (depending on soil type, possibly filter fabric and washed stone)

Inside the basin, a concrete paver is a suitable pump support. Don't put anything else in there that would make cleaning more difficult.

In my personal experience, pick a submersible sump pump - all the ones I've met have been much more reliable than the pedestal style pumps. To get the most out of whatever pump you buy, don't cheap out on the pipe size - plastic pipe is cheap, no good reason to reduce 2 inch threads to 1-1/2 inch pipe, but I see it all the time - even 1 inch pipe; don't do that - stick with whatever size the outlet on the pump is for best efficiency. And make sure it discharges far enough away from the building - I've met quite a few that pump the same water in circles, from inside to outside, where it comes back inside, to be pumped back outside...

Also, run the pipe straight up as high as it needs to go from the pump, then slope it towards the drain at 1/16 to 1/8 of an inch per foot (or 10mm per meter.)

If you are concerned about pumping rate, you can either try to come up with some sort of test flow (difficult unless the weather cooperates) or simply mount the pump to one side, so that you can add a second pump a few inches higher (use two pavers) if the first proves inadequate when the rains come. If you already have a pump in the old sump, start with that and see how it does.

The room in question is fairly large and has several heat loss factors. Not withstanding the fact that the room sits on the cold basement floor, has large windows etc., the main problem is that the temp in the room is not thermostatically controlled properly. The only thermostat and heat zone is on the main floor and controls heat based on temps in the main living space. Your typically closed bedrooms and lower level rooms will never heat or cool at the same temps as the room the thermostat is monitoring. If you really want to have accurate temp control, it may be necessary to install zones. One zone for open living areas (kitchen, dining, living spaces) , a zone for bedrooms, and a separate zone for the office level. Without separate zones, you cannot monitor and adjust temps in the areas isolated from the living space.