First question:
Your total restaurant bill is the items you have purchased plus the sales tax and plus the tip (if there’s any). Sales tax is added to your purchase because this is tax imposed to the consumer and not to the buyer. The buyer is only required to collect this tax from the buyer.
Second question:
A check is a financial instrument wherein the bank is required to pay when presented or encashed to them. You just have to make sure that you have account balance to that certain bank.
Third question:
The way of payment not any more common in the most modern economies is the bartering. Both credit cards and cash are the most common way of paying for your purchases.