Sometimes only one is possible; I think you just have to learn the individual words.

This is probably not a reliable guide, but where both exist, the "-ic" form sometimes expresses the nature of the qualified noun, whereas the "-ical" form is used when the qualified noun is related in a wider sense, such as "concerned or dealing with" (for instance: "electric power", "electrical engineer"). Here, too, I think you have to learn the individual meanings (e.g. "classical music", "classic Hitchcock"; "historic event", "historical research").

Also usage may change with time.

When one form has become standard some authors may use the other form when they want to express something slightly different using their own definition.

As regards your examples, I, personally, would always use "semantic" and "theoretical"; and I would use "classic" and classical" with different meanings.

I agree with Mike#, you have to learn the individual words.

There are often pairs of words with different meanings: historic/historical, economic/economical, classic/classical.

und wie ist es mit publical und publically?

sorry, ich meinte publicly und publically

I don't think "publically" exists, at least not in BE.

public is a word, publical isn't.

I was surprised to discover that publically is a word. It's a variant spelling of publicly.

"Public" is a noun or an adjective. "Publicly" or "publically"[sic] is an adverb.

Bei den in #1 genannten Beispielen finde ich es nachvollziehbar, dass es einen Bedeutungsunterschied gibt (und vielen Dank für die Erklärung, sehr einleuchtend). Aber wie ist es mit symmetric/symmetrical? Gilt das da auch?

same problem here: phonetic vs. phonetical 'his phonetical analysis ...'

I'm editing an English article - not written by a native speaker - and don't know whether to correct it or leave it as it is.

I don't think 'phonetical' exists, although it doesn't sound all that horrible - just a little bit "off". There is the adverb 'phonetically'.

Consult an English dictionary(or 2!) if you need more information on specific words. I agree that you can't formulate any general rule about these variants.

sounds strange - I agree

the adverb phonetically is derived direct(al)ly from phonetic

Es muss heissen: his phonetic analysis

Danke : )

... its not like dictionaries - even the thick ones - always have all the words ... ; )

Ich habe noch eins:

Wie heißt es richtig?

the automatic assignment is unique ... (die automatische Zuweisung ist eindeutig)
the automatical assignment is unique ...

Ich tendiere zu automatic, aber der Text, den ich gerade korrigiere, enthält automatical.
Welches ist richtig und warum? Danke!

#14: Wie heißt es richtig?

automatic (I assume): "automatical" is a "non-word", IMO.

(Better late than never, eh! :-))