To browse a shop or to browse in a shop
From browse the shop, I would take away the meaning that one looked through the window, to decide if it was worth entering.
From browse in the shop, I would take away the meaning that the person was in the shop, to decide if any products were worth purchasing.
Browse the shop
Checkout the shop, investigate the shop, thorough look at the shop.*
Browse in the shop
Checkout the products in the shop, investigate the products in the shop, thorough look at the products in the shop.*
*As per my knowledge