George has addressed your heater problem - which sounds to me like crap stuck in the squirrel-cage blower shown in your photo. I suggest you get in there and clean it yourself, as this is common and you CAN fix it yourself and it DOES happen every now and then!

As to the window and top button issue - I think they are related:
You have one or two bad sensors in the top control system. The switch in the windshield frame, if it gets intermittent, will cause the windows to go down. The flashing of the red light is an indication that the Power Top Control Module sees one or more sensors in the wrong state OR that you are trying to put the top down without the prerequisites met for top motion. Read on....

That switch tells the Power Top Module (which then tells the Body Control Module) that you have turned the hand crank and are about to put the top down. SO, the BCM puts the windows down for you. If you grab the crank and turn it, then return it to it's normal position, the windows will start to go down, then stop going down when the switch goes back to normal as you return the hand crank to locked.

Sound to me like the switch is "jumping" from one state to another and the top module is just doing it's job - it is responding to the bad switch per design.

Again:
If the switch in the windshield frame indicates to the controller that you have the top open while you are going over 9mph, or don't have the trunk divider up, or don't have the trunk closed, then that light should flash indicating you (according to the bad switch) have turned the hand crank and have started to put the top down when you have no business doing so! I suspect that this is what is going on.

Summary:
You have one or more sensors that are lying to the top control module.

Your options:
1) Take it to a Chrysler dealer and leave it with them until about spring. They will try everything under the sun to fix it (except for logical electronic troubleshooting techniques, because no one teaches that anymore) and will charge you for every wasted hour and part they put into it. This will run $300 to $2500. The cost is in inverse proportion to the skill of those working on the car - this is where a well paid, skilled tech saves you money.

2) Take it to a competent shop - I have NO IDEA what is in your area.

3) Fix it yourself - one way is to show up at a GTG where some of the rest of us are, and we can try to help. Our GTGs are known for all the emergency repairs that get done.

There is one thing you can try: If the hand crank mechanism is loose and sloppy, the tongs that reach into the windshield frame will be loose and may allow the sensor to relax and indication an opening top. Or, the sensor is loose in it's mount and this is allowing it to relax and show a fake open condition. (The switch's actuator is held down by the tong on the top mechanism on the passenger side of the top. Whne you turn the crank, the tong moves away, letting the switch relax, the switch closes, shorting the wire to ground. When the top module sees this ground, it assumes that you are putting the top down.) If you partly open the top, you can reach in there with your finger and feel the actuator blade on the switch. Getting to the switch itself must involve taking the trim off from either the top of the frame of down below the frame, I've never looked into how to get in there.