It doesn't come with any connectors, but that is specific to the card manufacturer. I am using an HDMI cable for one monitor, a DVI cable for another, and a displayport to HDMI cable for the other. I still have one extra DVI port.
I never really check these things. They change from GPU to GPU, and I have yet to here the fan on the video card spin up full speed. When those fans start to run full speed all the time, I may check the temps, but the majority of the time I simply ignore it completely. When the fans are running full speed constantly, as if they are not cooling, you will know, and when it starts to become extremely unresponsive (sort of what you explained with your quadro), then you know you have an serious cooling issue.
Yes, you are defeating the purpose of an airflow with this method. The idea is an "enclosed space" which can hold a constant lower temperature than the outside, as air flows through it. Having openings like uncovered slots, and the side panel off, will cause everything to heat up; it will effect your motherboard temps a lot, and that is something you do not want
Again, I would suggest that you focus on just fixing your airflow. Once you fix that correctly, you won't have to even think of these things unless you plan to overclock your GPUs. I know a lot of people that run servers 24/7, in 100F rooms, and have no trouble at all, simply because their system airflow is good.
The airflow is something I would fix before even considering a new card at all. I do not mean to be so harsh about this, but if you get a card first, you may end up ruining that card. The reason would be due to a faulty airflow, and I would hate to see that happen. There are lots of options out there, you just need to pursue them when your festival is over.
My suggestions: Get a card slot exhaust fan to help your PSU on the lower half of the system, replace any fan that is not working, get a filter, and 120mm or 140mm fan for the bottom of the case to bring air into the lower portion, take the 520 out, or move it, since it's just blocking airflow to the quadro (what is it even used for?), and then cover the open card slots. Also, an additional option is to find a HDD case fan for the drive bay to help bring in more air from the front.
Here are all the fan sizes for your case, so you know exactly what to replace, If your side fan is not working, according to the site, you can replace it with two 120mm fans, which can be a better idea. Even though the 200mm fan can cover more area, the 200mm fans are very slow (600-700rpm), A matter of fact, there are other HAF users that recommend the 2x120mm fan setup for their 212 (it has the same side panel as your 922).
If you still have issues finding some things in your area, I'll contact my buddy Avanash over there, and ask him if he knows of any good places to find some of these parts.
Yes, sell the Quadro for sure, when it comes to that point. Although, I would just start with a single AMD R9 390. You've been using a Quadro 4000, and GeForce 520. With a single 390, and 8GB of memory, you are going to be blown away with the performance you get. I would advise just getting one, and see what you think about it. Use it for a month or so, and see if you really do need a second one, and if it will benefit what you do in Blender. After that month or so, the prices will go down even more.