After a couple of days more customers start to come in. In about 2 days there are so many customers that a lot of them get stuck and aren't able to leave in any way. This causes my game to lag and run on like 15 fps. Because there are so many customers I can't possibly read their requests. Is there any way I can fix this? Maybe a customer limit, different positions in the shop or a queue for the customers?

Based on my gaming experience. Every time you meet a customer who wants a shield.  If you sell something to him, your customers will add one more person. Refuse to serve customers who want shields would be better.