Why does the verb sometimes change when we go from declarative to interrogative?

I have noticed this error in non-native speakers more and more recently**, but I don't know how to explain it, i.e., I don't know what this phenomenon is called nor what the rule is. An example:

Does this work?

becomes

Yes, that works.

Note the change from work to works. I think generally this happens when we go from declarative to interrogative but I'm not sure. It also doesn't seem to happen to the first person:

Do I run every morning? Yes, I run every morning.

Does he run every morning? Yes, he runs every morning.

**The error is when people do not do this, e.g., "Yes, that work."

Solution 1:

[1] Does this work?

[2] Yes, that works.

In a clause like [1] the dummy auxiliary verb "do" is used to form the interrogative, and it's this verb that is marked for tense and person ("do/does/did"). It's not possible to have two tensed verbs in the same verb phrase, so the complement of dummy "do" must be the unchanging plain (infinitive) verb form, in this case "work".

Thus, in [1] the dummy auxiliary "does" marks the present tense, and "work" is the required plain form.

[2] is not an interrogative, so dummy "do" is not required. Here the tense is marked on the lexical verb; in this case "works" is present tense.

The same grammatical rule applies to the interrogative in your other examples, where dummy auxiliary "do / does" is followed by the plain form "run".

Note: the placing of an auxiliary verb like "do" before the subject in interrogatives is called 'subject-auxiliary inversion'.

Solution 2:

I don't know what this phenomenon is called nor what the rule is.

It is called "question formation in English"

It is absolutely standard. When you have a 'helper' verb, the helper verb is conjugated and the main verb keeps its infinitive form.

Here are the rules:

Question formation in English is different from the formation of other sentences in two main ways. https://www.englishhints.com/question-formation.html