Tables are fully documented in the File Layouts, linked from the launcher.

https://help-sage100.na.sage.com/2021/FLOR/index.htm#File_Layouts/Accounts_Receivable/AR_Customer.htm?TocPath=File%2520Layouts%257CAccounts%2520Receivable%257C_____27

do I understand correctly that BOI is the interface for ODBC? is it installed on the client's side and if yes, should they pay for the license? 

I am trying to understand how is BOI installed

If you are using ODBC, ignore absolutely every reference to the BOI (which is something else entirely, although they are both available when you install the Sage workstation software on a machine).

Open DataBase Connectivity is through the ODBC driver.  You know it is available for a machine when you can log in to Sage 100 and print (because printing works through ODBC).  For external queries you'll also see SOTAMAS90, as a reference of the connection string.

You really should be talking with the Sage Partner for the client, who can instruct you on these things, hands-on, in minutes.

BOI for most is a COM/OLE object interface. You can also access the BOI internal object framework with creative ProvideX scripting. ODBC access shouldn't have to be explained other than it's read only.