What's "way" mean here?

Does “make bank” mean “make a lot of money”?

Good question! Yes, "make bank" means "make a lot of money". Ex: My friend got a new job, I heard she makes bank. Ex: I've been making bank lately!

What's it mean by "here" here?

Here,"here" means "to this point," or this circumstance or situation, rather than physical location. Ex: I got here through hard work and motivation. = I got to this point in my life through hard work and motivation. Ex: I don't know how to get there. To a happy life. Ex: We never would have got here without you.

What's "house" mean here?

Here, "house" is a verb that means the place where something is kept or operates from. In this case, a task force. Ex: The new offices will house 50 government administration workers. Ex: The restaurant houses the best kid's play area in the city. Ex: Did you know the library houses 10,000 books?

Is it ok to use "make contact with people as little as possible" instead of "make as little contact with people as possible" here? Which sentence sounds more natural?

Yes, you can say, "we're just trying to make contact with people as little as possible." However, the sentence you proposed is a little wordy and long. Both are perfectly fine to use, but I think "make as little contact with people as possible" is a better choice.

Doesn't "breeze" refer to a soft and weak wind? Wouldn't it be awkward to say "strong breeze"?

Yes, a "breeze" is a gentle wind. However, we do say "strong breeze" quite frequently. Even though the words contradict each other, we still use this phrase. Ex: We are going to have a strong breeze tomorrow. Ex: The strong breeze blew through the trees.