Options Trading

I do have a question regarding options trading.

For example-Selling Put Option

Stock Price $25

Strike Price $23

Premium $1.50

Should the option expired in the money with the stock price lower than the strike price does like to understand the seller needs to recieve notification if the buyer of the options wishes to exercise to sell the 100 shares before the seller exercise to buy the over the shares?If that is the case how does the seller gets the notification and if the buyer does not wish to exercise then the options expire worthless and seller of the put options need not fork out the required amount right?

Secondly is it correct that when seller buys over the assigned stocks the amount he/she pays will be the initial price of the sell put strike price in this example case $2500 at the same time gotten the premium at $150?

Lastly selling a put option is the strategy where the stock price expected to rise and the put option is to hedge against stick pricing falling?And also will seller needs to buy over the stock if the strike price upon expiry is in the money & out of the money?