Learn English – What would you call a criminal who is responsible for driving a car and helping the others escape

The joke would be called something like a 'lead balloon'

There isn't really a specific word for a person who told the joke. Maybe just that they have a bad sense of humor. Humorless might work, although that might not be a good word if they at least have some sense of humor, they are telling a joke after all, tasteless works quite well, but this is quite subjective, a tasteless joke is always a bad joke but a bad joke is not always a tasteless joke. Tasteless is generally applied to jokes that are considered offensive (and unfunny by the person listening). Bad is generally applied to any joke that is not funny.

The feeling, I guess would be disappointment if you were expecting a funny joke or exasperation, annoyance. It really depends on the person and the context of the situation.

A reaction, again, would depend on the person and the context, based on the feeling.

You might say a range of things, again, this really depends on the emotions that the joke evokes(is that the right word?) out of the person, there isn't really a standard response to any joke, although particular types of jokes may have standard responses.

There is a related word, scapegoat, which means:

scapegoat (noun) A person who is blamed for the wrongdoings, mistakes, or faults of others, especially for reasons of expediency.

From this word, we have the word scapegoater, which means:

scapegoater one that makes a scapegoat of something or somebody

While scapegoat is fairly common in the vernacular, I think scapegoater is a less common word. However, it fits what you are looking for.

Here's a usage of it in print:

Tolerance and independent thinking are essential to a democratic form of government, but the scapegoater cannot think straight.

(Charles Henry Scherf, Do You Own Thinking, 1946)

Another book about hostilities in the workplace says:

A scapegoater is one who transfers blame to persons or groups, who are not necessarily guilty, in order to focus attention away from those who are actually responsible — sometimes from themselves.

(J.A. Wambach & R.W. Fuller, Battles between somebodies and nobodies: stop abuse of rank at work and at home, 2008)