In a cash game, the house takes chips from each hand.
What is the formula? Sometimes they take $1
Other times they take $10 or more...

It's usually posted.

Something like 10% up to $5 max. Some places round up, some down, others also have an additional $1 that gets taken for a jackpot (usually at $20 in the pot, but again it varies).

Is a $5 max for a 1/2NL table pretty standard?
You're saying for general hands it's 10% + $1 ?

This varies greatly depending on the casino.
At a 'typical' casino they take 10% rake.

At $10, they take $1.
At $20, they take $1, (for $2 total).
At $30, they take $1, (for $3 total).
So an on so forth until they reach whatever their maximum cap is.

Some places also take a bad beat, or promotional drop, which they can take whenever they want based on house rules.

Any casino you go to should have the rules posted as to when they take their rake, how much they take and how they use any promotional $'s. If they don't, just ask.

But it varies greatly from place to place, so there's no one answer.

The normal max on the east coast is $4-$5. I don't know about the west coast. I think a lot of Vegas is $4 also.

$5 max + $1 BBJ is pretty standard. Most casinos do 10%. My home casino does 5% up to $5. (.50 for every $10 in the pot, capped at a $100 pot)