Hi Hyomin, hope you're well.
Ooh, this is a fun question!
Ok, so the first sentence.
"We'll come pick you and your wife up in an hour."
There are three different verbs in the sentence.
We have 'WILL', our auxiliary verb, to show that it's future. 'COME' is our first verb. It's in the basic form (bare infinitive) because it's following a modal. Then we have 'PICK UP', our phrasal verb (a verb + a preposition).
'PICK UP' is a separable phrasal verb, meaning we can put our OBJECT (you and your wife) between the verb and the preposition.
The original sentence would be "We'll come and pick you and your wife up......"
However, this AND is not really necessary. It can be understood from the sentence. So, we drop it.
"We'll come pick you and your wife up..."
This is a feature of English called ELLIPSIS. It's used for a number of reasons including to be more dramatic and sometimes just to be a bit lazy.
Be careful though! We can only do this with two basic verbs, i.e We'll COME PICK...
This sentence in the past wouldn't work.
"I came ate dinner as soon as my mother called me."
As the verbs are in the past, it would have to be "..came AND ate.."
But it WOULD work in the future.
"I'll come eat dinner in a few minutes. I'm just finishing my homework.
Hope this helps you :) It was a great question!