Do businesses make a profit on VAT?

Generally: No, only if they commit VAT fraud.

Basically, VAT is money for the government. The business collects it, deducts the amount of money it PAID for VAT, then sends the rest to the government. If the result is negative (because you have more VAT expenses than income - which may happen i.e. if you export out mostly to countries that are outside the EU and so there is no VAT on the sales) - the government will return the balance to you.

There are some VERY few exceptions, and those basically are if you run a business that is in a category that can not deduct VAT. VERY small list. And then they basically do not collect VAT.

Does it mean they keep the extra $1?

No, it means that they have 1 USD to send to the government to balance the VAT account.

VAT is always a pass through for the government. The only way it impacts you as a business is if you run a VAT deficit and the government takes months to refund the money (without interest).

You can make a bit of money in the UK on VAT if you are a very small company (one man band). If your revenue is low, you can get a deal where you register for VAT so 20% is added to each bill, but you don’t deduct itemised VAT but are allowed to pay only say 14.9% of the bill including VAT. So you can put about 2% or so in your pocket, legally.