A family of Microsoft relational database management systems designed for ease of use.
Again, Access is not a spreadsheet. Access is a relational database and you should use it relationally as it was intended. Using Access with a single table is a waste of time.
You refer to a query, but with a single table I don't know what you need a query for. You need to understand how a relational database works and how to normalize a database. And the first thing you need to do is stop thinking and referring to it as a "sheet".
At the very least, based on what you have said, you need at least three tables:
tblChecks
CheckID (PK Autonumber)
CheckNumber
VendorID (FK)
CheckDate
CheckAmount
SiteID (FK)
tblVendor
VendorID (PK )
VendorName
other Vendor info
tblSite
SiteID (PK)
Sitename
You may need more.
As for only allowing the sites to edit their own, you should have a login that identifies which site and then filter the form soo they only see their site.