Can I get a settlement if I cut my arm at a store while in the process of avoiding an employee?

Your injury is very minor and, at best will only get a few hundred dollars.

It depends if the employee was acting in a negligent fashion or not. It does not sound as though you have any type of permanent injury so you can not expect very much at all from the store even if they want to settle.

Possibly, depending on the details. As someone legally present at the store, you enjoy the special status of being a "licensee" or, in some circumstances, an "invitee." If your injury was caused by the store employee's negligence (for example, failure to keep a look-out) or was caused by a defect in the premises (for example, inadequate lighting or protruding metal shelves), you may have a claim. On the other hand, the store is not an insurer of your safety. Nor is the store responsible if your injury resulted solely from your failure to keep a look-out or exercise reasonable care for your own safety.

Probably not.

This is one that could go either way. You have to show that the store employee was negligent, that he did not take reasonable care for the safety of the customers, that he knew or should have known that his actions could result in customers being injured by trying to avoid him. Here's a tip: when you say "I had to avoid running into an employee..." it sounds like you were doing the running and so created the hazard, making the event your fault. When you say that you were "in the process of avoiding an employee" that indicates the employee was coming at you, and so you had to avoid him. It's a simple turn of phrase like that that can turn a case around, which is why you need a lawyer.

My mother's advice in this instance would be apropos. Never run in the house.