How do you expect someone to check on an application if we can't call and can't email either. I guess walk in and ask for a manager is the only option after applying online.

Yes be proactive. I would say give them a reasonable amount of time to review your application maybe 2-3 weeks. If you haven't heard from them, go down to the store you applied to dressed nicely, and ask a store manager about the status of your application.

Will Aldi ever open a store in South Lakeland, Florida

Yes if you can't call or email the best thing is to go in personally and ask the store manager. If that store is hiring going there and talking to the manager will be the best it will show the manager that your interested in the position and remember go in dressed nicely that helps a lot also.