Replaced bathroom fan timer, risk of fire???

There should not be a heat problem, but it sounds like you have too many connections and devices for the work box size. The extra size of the digital control may have taken too much.

Unless one of our professionals say otherwise, then I would suggest you are ok for now, but if you have to open it up again, I would consider replacing the existing box with a larger one. Trying to squeeze too much into a too small box can result in stress on connections that may cause them to fail. But that would generally happen only when you are working in the box.

There is a chance that you may have caused a partial failure and that could cause extra heat due to a poor connections. With the typical loads (without a heater) in the usual bath fan application it is not likely to be a problem. However if you have a pass through, then again it could be a bigger problem.

In short, I would likely leave it until I had to work on it again, some would not bother not matter what and some may tell you to go back now and fix it right. I will defer to those who work in this stuff and know the national codes.

No problem. That's why the box is metal - if a fire breaks out, it will be contained within the metal enclosure. Most of the time.

You are correct. If I were you, I'd just dump a gallon of gas under that timer, toss a match and collect the insurance money.