2003, air locked/clogged heater core?

Hello, two days ago I installed a new water pump and thermostat, as well as performing a multi stage coolant system flush(before installs) after having an overheating issue the other day. It was the original water pump and thermostat with over 140k miles on it so I figured what the hell let's give it a swap. After performing the correct bleeding process of leaving cap off, closing bleeder valve, running engine to warm while filling up as much as possible. Then cooling, bleeding the air repeat( hopefully that was the correct process lol) I realized tonight I have no heat at all. The temp gauge was pegged in the middle after a 20 minute idle, drive, then idle in the garage for an additional 5 minutes wondering if it would kick on. I had a hell of a time trying to keep the thermostat in the housing of the upper radiator fixture that connects to the front of the intake. I used rtv blue to make a gasket. All contact points were cleaned and resurfaced using an air power wire brush. I'm wondering if my thermostat may have slightly fallen out of it's extremely small placement lip inside the upper radiator fixture and is somewhat "stuck open". I don't believe I am leaking any coolant. I've only noticed my small oil pan leak after the car is shut off which I'll worry about soon. Or. Do I still have air in the system. This is all my very first attempt at any repair work period on any vehicle. I purchased this vehicle to learn and have a hobby for the next 10 years lol. Since all the installs I have had zero issues with temperature. Hell..it takes 10-15 minutes to get up to optimal operating temp and has not even budged past the middle point on the gauge. I noticed today that the radiator fan will not kick on at all and after further inspection of the fan it clicks very loudly with a very minimal amount of force from me spinning it with my hand. It also feels very "geared" so I have ordered a new OEM spec fan from American muscle to be delivered on Wednesday.

My main concerns and questions are. Am I okay to drive it until the fan gets here with the temps in Indiana being VERY winter like still. Highs of 50-60, lows of 30 still.

And should I continue the bleeding procedure for the foreseeable future until it is absolutely filled to the brim. I fit just almost 3 gallons of coolant after the flush I believe.

Do I have a clogged heater core? The original coolant after drainage and flushes was somewhat dark green. I also noticed what appeared to be slight flaking and pinholing inside the old water pump, which yes, I know, is very scary but it is very minimal. I got it for dirt cheap, so I'm not too bummed that the previous owner/owners weren't the best caretakers of her. But she's got a new owner who will now lol

Sorry for the extremely long, overly descriptive message lol

Thanks, I'll save that link. Luckily I had figured out the correct way a day or so after my original post, she runs good and I've been driving her everyday since the entire cooling system rebuild/replacement with the temp gauge not once budging past half way. Coolant is still filled to the brim in the radiator, as well as proper cold/hot levels in the reservoir. So no leaks on the coolant side of things. To my knowledge my head gaskets are okay. Only issue I have now is a leaky oil pan gasket, but it only drips a half dollar size puddle after the engine is off, that'll be my next project.