There are two ways to save records.
Data in a sheet is saved altogether. If an error occurs in any record when saving data, no record is saved. The error detected first is returned. This is a specification imposed by kintone API.
When an error occurs, you can save only normal records by saving them by record basis from the context menu as described in 2.
When more than one user works with data, the behavior is same as kintone (see "Basic of App Features" in kintone Help Center for details).
If they edit different records respectively, they can save them successfully. If they edit a same record, the data edited by the user who save it first is saved. The user who tries to save the record later cannot save it and will receive the following error message.
"The specified revision is not up to date. Another user may have updated the record. (kintone error code: GAIA_CO02)"