do you latch the latch?

A: Lock up before you go upstairs. Don't forget to latch the latch.

B: How does this thing work?

A: Just push the knob to the right. EDIT: Just slide the bolt to the right.

B: There you go.

A: You forgot to latch the chain.

B: What do I do with the chain?

A: Just insert the end of the chain into the little hole above the latch.

B: It doesn't fit.

A: Insert it on the far left, where the hole's bigger.

Do you latch the latch?

Do you latch the chain?

EDIT: I just saw this on my searches. Could the picture be a deadbolt and not a latch? If so, do you latch the bolt? How about bolting the bolt/deadbolt?

You'd fasten the chain and set the latch.

No, it's not a deadbolt. A deadbolt needs a key to get out as well as to get in.
https://en.wikipedia.org/wiki/Dead_bolt

The picture shows a type of bolt lock.

Your question is hard to answer because the usual conversation would be about locking the door, not doing something with the lock. When you ask whether someone locked the door, you don't care what kind of lock was used.

I just want to share what I learned, as well as for confirmation.

The caption for the above picture is Old Fashioned HD Hinges, Warwickshire Latch and Cane Bolts.

So I gather the lock at the upper portion of the gate is called a latch, while those thin bars that stick to the ground are called cane bolts or drop rods (found this other term on my searches).

The action related to latches is to set the latch. Question: Do you unset the latch or unlock the latch?

The action related to bolt locks is still set the latch. Question: If it's called a bolt lock, not a latch, why is it still set the latch? Would slide the bolt be more appropriate? Can you say lock the bolt or bolt it?

Would the action related to cane bolts be bolt the canes, while you could say drop the rods if you call those drop rods?

Conversely, do you unbolt the canes and pull up the rods?

Which is a more common term, cane bolts or drop rods?

I had to post a video because I really couldn't find a picture of the above. You don't have to watch the entire video, the action I'm concerned about is on 0:13 mark.

So, from the title of the video, that latch is called a bolt barrel, is it correct? Or is it just called a bolt lock, while the barrel refers to the loop the bolt slides into?

The action the man was doing would be called sliding the bolt, would it not?

To be more specific, the man is moving the handle up and down while sliding the bolt, correct?