Short answer - YES. The store will cut panels to your needed sizes. Take your cut list and watch them cut.
Most MDF boards contain toxic chemicals including formaldehyde. Definitely use proper precautions.
Several conditions to consider If you are making flat panel doors using euro hinges, then the answer is no. The 35mm hole needs to be 1/2 inch deep. Any other hinge, yes If you are using this for a frame and panel door with a 3/4 inch thick frame with euro hinges, then,yes, that would work.
If nothing has changed because of the pandemic, they will cut your panel to size. There should be no cost. Hope this helps.
I wouldn't, it soaks up water like a sponge and doesn't hold staples strongly.
If you cover it with laminate, it might work but I would opt for 3/4 in plywood instead.
Short answer, yes. There would be many, many cuts - could be a small charge because of the unusual number of cuts. It would not be a prohibitive cost.
Most Home Depot Stores will make a few cuts free. Check with your local store on their policy. I have often had 4x8 sheets cut without a charge.
Yes it can. can you seal it or a good paint on it? even with a little moisture, over time it will show signs of damage in a few years.
They won't be able to even rip it to that size. They have a safety rule that they won't cut anything more narrow the saw guides. Which is about 6 inches.