Learn English – Why does the phrase “cross the fingers’ mean just “cross middle finger over index finger”

I can understand why the connection between these two senses of "dispose" seems so mysterious. The key to understanding it is: "to get rid of" is actually a secondary sense, even though today it is very common. The primary sense is "to put things into their proper places". The primary sense is now rare, but it still colors and explains the secondary senses.

Putting things into their proper place

When you dispose of garbage, you put it into its proper place: a garbage can, the city dump, or someplace like that. When you dispose of radioactive waste, you put it someplace very far away from people. However, throwing away garbage is only one of many ways that things can be "disposed of".

I marveled at the ability of a South China crime boss to dispose of these resources and organizational refinements with such precision. [Source]

Here, "dispose of" doesn't mean "get rid of" those resources, it means to put them to work in a coordinated manner—that is, to bring them to the proper places for performing some large, coordinated action.

In the Order Disposal Problem:

A manufacturer … may receive and dispose many production orders during a time period [but] he can dispose at most one order at any time due to resource constraints.

the word "dispose" means "to complete a job"—another way in which something can be put into its settled and proper place.

Being ready to act

Here is an example of saying that someone is disposed to act in a certain way:

Virtually all soldiers at all times have been strongly disposed to obey orders to go to war irrespective of whether the war has been just or unjust. [Source]

This calls upon another secondary sense of dispose: to put into a state of readiness to do some action—the action that one is disposed to or toward. The elements of one's mind, one's habits, one's abilities, one's resources, one's knowledge, one's surroundings, etc. are in a configuration that makes one especially ready to perform the action. This sense also occurs in sentences like this:

His generation and his origins dispose him to be a democrat. [Source]

Figuring out more senses of dispose

The word "dispose" gets used for many, widely varying meanings—more than I can list here, and indeed more than you'll find in dictionaries. Once you understand the primary meaning, it becomes a lot easier to understand how people are extending that meaning to fit different situations.

I think it helps to know the etymology, both for understanding the many senses of "dispose" and for many other words that contain the same two roots: dis- and pose. "Dis-" (in "dispose") is a Latin root meaning to break apart and spread out, as in disperse, disseminate, dissolve. "Pose" is a Latin root meaning to put something in a certain place or state, as in position, opposite, repose.

Knowing that, you might be able to figure out that a disposition can mean both an inclination toward doing something and the result of doing something—"where" things ultimately got put. The latter sense is rare, but an example is that in computers, a task is sometimes said to have a "disposition" of succeeded/failed/aborted. Another one is:

I can put five employees at your disposal.

This means that I can bring five employees to the appropriate place, where they will be ready to do as you command.

And finally, here's a stock phrase which is worth knowing, because it sheds a lot of light on the other senses: propose and dispose. Here's an example:

Men propose; women dispose. [Source]

This means that men offer possibilities to consider (propose), and women decide which proposals to carry out and which to reject (dispose—that is, sort out the proposals and bring some but not all to action).

In the etymology you've posted, 'fun' is described as "to cheat, hoax" as early as the 1680s. 'Funny' is then attested at a later time as a modifier with a slightly modified sense emphasizing the humorous aspect of something like a hoax or joke. A particular 'cheat', 'trick', or 'hoax' could seem more like a good-natured laugh or more like a mean-spirited attack. You see this spectrum of meanings in the various definitions.

At it's core, 'funny' means 'unusual', 'unexpected', or 'odd'. All the definitions you've included in your questions are just different, more specific ways in which it is used to mean this.

Humorous

Things which are completely expected, known, and ordinary are generally not funny. Most humor involves misdirection and surprise, so it fits in with the ideas of unusual and unexpected, i.e. 'odd'.

Strange

I hope this is clear.

Dishonest

Things or people which are dishonest are not what they're expected or believed to be. Some uses of 'funny' in this sense include "funny money" and "funny business".

Unfriendly

I'm not familiar with this usage, but I'm not from the UK. The closest thing I can think of is "you're acting funny" when someone seems to be offended. This is said because the person is not acting in their usual manner, but instead in an offended manner. I suppose this could be extended to general unfriendliness fairly easily.

Ill

The important thing to note here is that 'funny' can mean "slightly ill". Feeling funny is between feeling healthy and feeling sick. You don't feel like you normally do, but you don't feel awful either. A simple stomach ache probably doesn't go beyond feeling funny, but the flu takes you all the way to sick.

A synonym for this sense of 'funny' would be 'quesy'.

Crazy

Crazy things are so unexpected and unusual that we often can't figure out why they would be that way.