The date format is not really a problem in that the actual date value saved in the table is the same in both cases. That's true regardless of the database in use. I assume that Dataverse is no different in this regard although there other, more problematic differences.
However, you are using Dataverse, which imposes a degree of overhead in the way it handles things. Check the settings in your M365 account where the Dataverse tables are located. Perhaps you can adjust regional settings there. You may need assistance from an administrator, depending on how the account was set up. I don't know how to advise you on finding it yourself, unfortunately. M365 is a labyrinthic maze to navigate unless you live and breathe it as an administrator.
With regard to your second question, you might be able to work around that limitation in Dataverse by requerying the form's record source. Apparently a refresh isn't effective for retrieving other records not present in the record source when the form opens.
Since the issue is with records added by other users, you might need to requery the source prior to initiating a new record addition/update by the user.
How is performance otherwise compared to a local accdb back end? Or an accdb back end on a network location? How many records are in these Dataverse tables? I ask because it is frequently reported that performance can be quite unsatisfactory with Dataverse and large recordsets.