1. Do you have walls? If it says Walls x0 in the inventory you can't place anything. I made it so the first purchase in the shop "unlocks" the item, but you need to buy once again to actually buy them. (Probably bad game design on my part)
2. I think it can be buggy sometimes but I can't reproduce this error, try switching to shooting mode and back to build to see if it works. One thing is you can only place within a specific area (which I unfortunately didn't have time to show as a QoL feature), try placing in the middle to see if that works. Sometimes just clicking might not work, so hold down left mouse button.