-ic vs -ical

Some of those are not legitimate words, like "horrifical" and "feministical", but I see your point. Why there are two forms, and if there are any differences.

I think you have to look at each pair / trio separately; I don't think you can draw a hard and fast principle that covers all. I agree with Dyske about horrifical and feministical, so let's look at the rest, starting with the easiest ones.

ecclesiastic - only a noun
ecclesiastical, ecclesial - both adjectives, and apparently synonymous. The latter seems to be very formal and apparently was rarely used before the 1960s (Oxford) - I'd never heard it before and it's not in any of the five advanced learner's dictionaries I checked. I think this might be mainly and American usage.

fantastic and fantastical - both adjectives, and for the meanings of 'strange and showing a lot of imagination' and 'impossible to put into practice', they are synonymous, but of course, fantastic has other meanings, such as great, brilliant, amazing, etc, which fantastical doesn't have.

The difference between comic and comical as adjectives is the most difficult to explain. For categorisation, we use comic - a comic actor, a comic opera, a comic genius etc. Comical is used more for situations, and my dictionary suggests it has an extra meaning - 'funny or amusing because of being strange or unusual'. When we use it about people it has a bit of a negative quality, I think. We laugh at somebody who is comical, rather than laugh with them.

Comic: intentionally funny
The clown performed many comic tricks.

Comical: unintentionally funny
The man's attempts to find his train ticket were comical.

If you look at the etymology for a few of these valid words, you will find that the -cal version came from the -cally adverb form of the noun. It's just one of those linguistic evolutions that stemmed from -cally being more palatable to writers/speakers than -ckly whenever the elusive powers that be decided on the fate of these words for English.

Since this is the case, I guess you could probably say that any word that spawned from its -cally form has essentially the same meaning as the -cal form. As Warsaw Will mentioned, though, this is definitely one of those case-by-case things, simply because of words like horrifically that do exist without their -cal adjective forms. If you do a search, though, you'll find that this is one of those lines that you can cross and get away with (like dangling prepositions). There is no formal definition or acceptance to horrifical, and I would be embarrassed to use it myself, but ask Shakespeare about how scared he was to fashion new words from playing like this - he probably structured and cleaned up more gray areas like this one than we know.

In the study of electricity, the words "electric" and "electrical" are often completely interchangeable. Otherwise, sometimes one of these is customary to use, e.g.
"electrical engineer" and "electric motor".

D.A., I'm chuckling right now over the thought of an "electric engineer." Whether that would refer to his/her personality, dance moves, or what causes the engineer to move (if the engineer was electric, it seems likely the engineer wouldn't be human).

In terms of "electric engineer" and "electrical engineer", I would love to give my thought too, I have more than once seen native speakers interchangeably. using a "historical character" and "historic character". Which one should be more accurate?

Had to chuckle at Eucharistical. Never used.

While there may be some overlap, I think of comic as meaning "of or relating to comedy" and comical as "in a comic manner", i.e., funny. I think this is often the case with -ic vs. -ical. Wow, glad no one asked about comedic!

I think that comic as a noun grew from the adjective. Funny how often this happens. Compare music (really adjectivally from "of the muses" even though it's never used as such) and musical.

I've also thought that animal as a noun arose as a "nounification" from the adjective animal (of anima), but I'm not sure this is etymologically correct.

@porsche - according to Online Etymology Dictionary you're absolutely right about animal. We apparently got it (via Old French according to Dictionary.com) from the Latin animale (n) "living being, being which breathes," the neuter of animalis (adj) "animate, living; of the air," which in turn came from anima (n) "breath, soul; a current of air".

Similarly, it has comic as an adjective from the 14th century, but as a noun only from the 1580s.