As you have likely learned, German verbs often use prefixes that change their meaning compared to their original root words. Usually, the prefixed verbs have a related meaning, however. For example, sagen ("to say") is related to besagen ("to state") by the fact that both words are related to speaking.
But in some cases, the relation of a prefixed verb to its root word is not so clear. For instance, untersagen means "to forbid," which in most usages refers to a law or rule rather than a verbal order. Its adverb strays even further from the root word: Es ist untersagt, den Raum zu betreten ("It is forbidden to enter the room").
Many such prefixed verbs are centuries old and stem from Middle German. They may have started off with a strong relation to their root words, but as time went on, the meanings of the words may have changed. Perhaps untersagen came from the days when a Saxon chieftain ruled the tribe by verbal command rather than by written laws?
Wir freuen uns immer, wenn Ausländer Deutsch sprechen.
We're always glad when foreigners speak German.
Caption 32, Anna: Am Strand in MexikoPlay Caption
Und auch die Tierstudien widersprechen sich.
And even the animal studies contradict each other.
Caption 17, Terra X: Anti-Aging durch Fasten?Play Caption
Sie müssen einen Kunstkörper herstellen für Präparate, die dem Original entsprechen.
They must make a plastic body for mountings that correspond to the original.
Captions 25-26, Wettlauf gegen den Verfall: Beruf PräparatorPlay Caption
The verb sprechen is the root word of many prefixed verbs that have at least a tentative relation to speaking: absprechen ("to agree"), durchsprechen ("to talk over"), or weitersprechen ("to continue speaking"), for example. But while people can contradict each other verbally, you see above that widersprechen can also be used in contexts far beyond those containing speech. And the verb entsprechen goes even further away from its root word sprechen.
Er läuft Runden im Park, bis die Beine versagen.
He runs laps in the park until his legs fail.
Caption 21, Maxim: Meine SoldatenPlay Caption
The primary meaning of the verb versagen is "to fail," and is pretty far removed from its root word sagen. However, the secondary meaning is "to deny (something)," which has stronger correlations to the root word: Es war uns versagt, den Raum zu betreten. ("We were denied access to the room.")
Die Hochzeit würde also stattfinden.
The wedding would indeed take place.
Caption 45, Märchen - Sagenhaft: Hans mein IgelPlay Caption
It's difficult to reconcile stattfinden ("to take place") with finden ("to find"). The noun die Statt is an old-fashioned word meaning "place," but it's unclear how "to find" is related to the meaning.
Es gibt keinerlei Hinweise dafür, dass Flüchtlinge öfter Straftaten begehen als andere Menschen.
There is no proof whatsoever that refugees commit crimes more often than other people.
Captions 42-43, Flüchtlingskrise: 10 Vorurteile, die nicht stimmenPlay Caption
Eine Straftat begehen means "to commit a crime," and einen Fehler begehen means "to make a mistake." On the surface, there is little correlation with gehen ("to go").
The Digitales Wörterbuch der deutschen Sprache (DWDS for short) has a good section on the etymology or historical origin of German words, but in most cases, they too have difficulties making tentative connections with a lot of the words above.
Read this blog about how German prefixes alter the meanings of words. You can also search the Lessons on Yabla German for various conjugations of the verbs listed above to see them used in different contexts.