As a new business owner who does not have the credit card processing machine, can machine leasing company sue me?

It depends on the lease agreement and the purchase agreement if you bought the assets and liabilities. Contact an attorney if needed.

Sure. Whether they win or not is the question. Did you buy the assets or the ownership of the company, i.e. stock for a corporation or the LLC membership interest for an LLC? If the former, you do not owe for the machine, because you did not take on the company's liabilities. If the latter, yes, your company probably do owe for the lease and the value of the machine.

If the business is a corporation, and you bought the corporation, the debt is still due. If the business is not a corporation, and you merely purchased some assets, and you are now a sole proprietorship, you are not personally liable for the contracts by the prior owner. This answer is based on the assumption that you are in GA. Since you said "I no longer want them to withdraw money from my business account" it appears you are using the same bank account as the prior owner. You should not do that. You are subjecting yourself to all issues the prior owner may have had with that account, including outstanding debits like this, bad credit card charges, bad checks that may come back, etc. If so, close that bank account and open your own account in your name. If you continue with the same account, you likely will continue to pay for the credit card processing machine.

Ask the company for a copy of the contract so you can see whether it binds you as a purchaser of the business. Did you purchase the old business name, XYZ, LLC, or did you purchase the clients, building, inventory, etc?