Other questions

Hello, just want to confirm, so if the invoice has been received by the vendor and will not be paid yet, so this will be tagged as "bill" in the projects section, right? but, if this invoice has been paid already, this will be added to "expense", right? what about if I want to pay the invoice that was initially inputted as "bill"? what should I do? 

Also, will the client see if I want to add these expenses/bill in the project section? I don't want this to be seen by them as, of course, there is a mark-up, what should I do? Is ticking on and off the "billable" in the the category details section will do this?