About bank account
As Lloyd had stated, you should have little problem opening the bank account in Florida for a Wyoming LLC. You may however have to travel to Florida to do so, as banks typically require applicants to appear in person. We have a research article titled 'U.S. Bank Accounts for Non-U.S. Residents' which may offer some helpful suggestions to help you accomplish this remotely.
You would need to file as a foreign entity in Florida if, for example, you decided you wanted to open an office there, hire employees, or use a warehouse to store the products. If you are simply shipping products to your clients in Florida from your company's website, then no, you would not need to file your WY LLC as a foreign entity.