No heat

Be sure both heater hoses are getting hot, If only one is hot you may have a plugged heater core or heater control valve that isn't working.

Read the guide below, it will help.

https://www.2carpros.com/articles/car-heater-not-working

The heater control valve is pictured below

Get the radiator and heater core flushed and retest.

If the radiator is clogged badly, you need a radiator shop to perform the job as the radiator has to be serviced.

No flush kit would be able to clean the engine with a one time flush.

Heat from engine operation works well to flush out the system. Try doing it without any flush kit first. Use water to flush out as much as possible and disconnect the heater core to back flush.

Reconnect and top up with water. Run engine without radiator cap and heater at maximum heat for a about 5 minutes, keep topping up the water till it stabilises. This is to bleed the system of air.

If water tends to gush out, stop engine and wait a few seconds to allow air to escape. Once level stabilises, close radiator cap and run to operating temperature for a few minutes. Allow to cool before removing the radiator cap.

You need to repeat this flushing and bleeding process a few time to get the stuck grime inside engine to be cleared. Once water seems to be rather clear, You can either use the radiatro flush kit or if you feel that the system is sufficiently clean without necessity of further flushing, drain and replace with coolant.

Ensure bleeding is done correctly and replace hoses that are not in good condition.

I would say that you have an air lock in the heater system, try bleeding the cooling system with the front of the car elevated slightly, when the heater is purged of air, with the heater on, both hoses going to the heater will be hot to touch.

Well the temp gauge is on the other side of the the thermostat, which means if the thermostat is stuck closed then fluid is not getting to the heater core, nor is it reaching the engine coolant temp. Sensor, so try changing out the thermostat. And let me know how it goes

I'm not understanding what you mean by "water ends up in the reservoir"? There should always be coolant in the reservoir.

As for the heat, I'm assuming your blower and dash controls work fine. If the heat isn't getting hot enough, could be a partially blocked heater core, a leaking vacuum line/solenoid in the HVAC unit and/or a stuck blend door.

Check the following: thermostat, heater core, heat control valve if it has one and also if the air blend door is opening to the heat position-start ere