Price protection with limits vs stops

Q1. From what I’ve read a stop initiates a buy or sell order once a tick goes beyond a certain price. I assume if your buy stop is $1.5, and subsequent tick is $1.6 followed by lower $1.45 or higher $1.55, you will get the market price and buy stop of $1.5 can get potentially fulfilled even at the possible lower price of $1.45, correct?

Q2. Do limit orders fulfill with price “protection” or without, as stops. When I place buy limit of $1.00 market is $1.30, following tick drops to $0.80 and subsequent tick immediately jumps to $2. Fulfillment at any of these prices is possible $1.00, $0.80, $2 or am I “guaranteed” a price at or below my buy limit of $1.00?

I’m submitting this question to broker so such a suggestion will be useless. How does your broker fulfill?