Basement egress through office

Before going through the trouble of an egress window, make sure the water problem is tackled. That, itself, can be a huge chore.

And egress window CAN be DIY, but it's going to be a lot of messy work. You need to move a large chunk of soil, cut concrete, install a well, and given the water issues, likely a dry well or drain system of some sort.

But yes, it can be DIY. I would worry about bowed walls, however. If the foundation walls are bowed inward, that can be a sign of huge water issues, as well as structurally compromised foundation walls. Before you dig around the foundation, you may want to consult with a structural engineer first.

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.