Learn English – would rather eat or ate

As written, both sentences could be used to state that one does not want to go to a particular concert and would like to stay at home instead. The first is mildly unusual for American English conversation, but not overly much - nobody would comment on it and everyone would understand what you meant. The second is more often used (in my experience). With a small modification to the first statement a significant difference can be seen.

Suppose we change the first version to the following:

I prefer staying home to going to concerts.

Here we're saying that as a general rule we do not like attending concerts and would prefer to stay at home. It doesn't matter which concert, we don't want to go. In my experience this construction, using gerunds instead of infinitives, is used primarily for generalities.

The second statement is more natural sounding, though it is a bit more formal than what I normally hear in conversation.

I'd prefer to stay home (rather) than (to) go to the concert.

This refers to a specific concert that I do not wish to attend. If I changed it to a concert instead of the concert then this would have the same generality as the first version, and it would still be idiomatically correct. The parenthetical "to" is usually omitted with simple statement where the comparison you're making is obvious. In a more complicated sentence (perhaps using longer technical words or a particularly long phrase as the first item being compared) it would probably be included.

For American English conversation, the following is how this sentiment would likely be stated.

I'd rather stay at home than go to the concert.

You are correct, the idiomatic expression is

I had a quick lunch.
I grabbed a quick bite to eat for lunch

in the same way

We had a working lunch

The reason for #4 is the adverb "quickly"

ate quickly

is much preferred over

had quickly