You can make anything a sinking fund. Maybe it's home expenses, vacation, major discretionary purchases. You pick the categories based on what you need.
You can open an account where you hold your checking account but it needs to be a separate account. Try a high-yield savings account for extra savings.
Make a budget and determine how much you can afford to save and how quickly you need to save to meet your goals.
You have lots of options to automate transfers. Check out apps that round up change, your employer options, and automatic bank-to-bank options. It's the best way to ensure you stay on track.
Some people will have 1 or 2 sinking funds, others may have 5. You need to keep track of how much is in each sinking fund since all of the money goes into one pot.