You are correct @fametop. Such omissions and substitutions are tested in comparison based sentences. You may also find the same in parallelism based sentences as well. Let's begin the understanding using some simple examples:
Tom solves SC questions more efficiently than Marie does.Here "does" is used in place of "solves" - Substitution
Tom solves SC questions more efficiently than Marie.Here "does" has been omitted. The verb can be omitted from the comparison since the sentence does not result in any ambiguity after the omission. So as you can see above, such omission (also called as ellipsis) is done to make the sentence more crisp. And how do we make the sentence more crisp - by not repeating certain words that have already appeared once in the sentence. This applies really well when we have comparison or parallel constructions involving verbs. And hence we come to the main take away.
You can omit the words till the point the meaning is clear.
Lets take another set of sentences:
Tom adores his wife more than his mother does.Here "does" is used in place of "adores" - Substitution
Tom adores his wife more than his mother.Here "does" has been omitted. But is the meaning clear? What is the comparison here? Are we comparing how much Tom adores his wife vs how much he adores his mother. Or are we comparing how much Tom adores his wife vs how much his mother adores his wife. That is one of the two following sentences:
1: Tom adores his wife more than his mother does.
2: Tom adores his wife more than he adores his mother.I hope this example set helped reinforce the takeaway stated above.
Now lets take up the examples in your question:
I have never seen an aardvark, but last year my father didNow this sentence is wrong. And here is why. Here ellipsis/omission has not been applied correctly. Basically the author has omitted the verb - see. (did see = saw) as shown below:
I have never seen an aardvark, but last year my father DID SEE.
But notice, the verb "see" does not appear as is anywhere in the sentence. And you cannot omit something that does not exist.
Now let's take this other example sentence:
Our cars were designed to inspire envy, and they areWhat could have been omitted here? There is a verb from "to inspire". So the verb form "inspire" could have been omitted. But when I place this supposedly omitted word what do I get:
Our cars were designed to inspire envy, and they are inspire. - This is absolutely incorrect.
Doing the same in the correct version - here is what we get.
Our cars were designed to inspire envy, and they do inspireNotice how putting back the omitted word makes perfect sense in the sentence.
Here are the other sentences in your post. I have specified the word that is omitted.
Megumi speaks Japanese better than I do
speak. - CORRECT
Megumi has visited more countries than I have
visited. - CORRECT
Megumi has more skirts than I do. - Here "do" replaces the verb "have" - CORRECT.
I hope this helps clarify your confusion!
Regards,
Payal
. Thank you.