1: The temperature rise for the heater will be from it's inlet-temp to output temp. The internal controls are designed to regulate the output temp. If your incoming water is 32F and it's programmed for 140F, that's what you get. (Up to it's max firing range, anyway). If you have a tempering valve or mixing valve on the branch to the domestic hot water to keep it at 105F, the flow throught the tankless will be proportionally lower. The delta-T in space heating mode will be much lower, since the return water from the coil will be above room-temp.
2: The safe bet is to go with a heat exchanger and keep the heating loop isolated. (Required by code in many areas.) But if the total volume of the heating loop is low, and is purged at least daily your risk of stagnant-water issues are low. If the fan coil and heating loop are plumbed in such a way that the incoming water MUST pass through the fan coil ahead of the water heater, the risks are essentially nil.
3: The fan coil loop would be driven by a properly specifed hydronic pump to handle the head of both the coil and the heater (or heat exchanger.) All pumps for potable water would need to be bronze, to tolerate the corrosiveness of fresh, oxygenated water. Iron pumps fail quickly when used with constantly replenished fresh water.
4: All tankless heaters modulate the flame based on input water temp and flow rate to deliver output water at the setpoint temperature. In space heating mode there's no input of 32F water, and the water entering the tankless will be 90-100F or more (depending on flow rate.)
This level of heating design isn't always a great idea to do as a DIY based on web-forum input, but the general approach CAN be made to work. I understand that in Whitehorse the heating system design talent pool isn't as big as in Vancouver or Montreal, but SURELY there must be somebody willing to take this on!?!
Also, why fan coil rather than hydronic baseboards, convecting radiators, or radiant floor or something? Hot air systems use more electrical power to distribute the heat, drive outdoor air infiltration, and are less adaptable to micro-zoning for better balance, etc.