Upgrading to Exchange 2013 STD on-premise. redirecting issues. DAG

I'm in the process of upgrading from Exchange 2010 STD to four Exchange 2013 STD servers. I'll be moving mailboxes to the new servers, as well as configuring DAG, High availability and Site Resilience. I made a few test mailboxes on both the current and new server. I was able to move the mailboxes from the current server to the new server with out any issues. Sending and receiving messages from the new server is working but I noticed if I attempt to access the mailboxes on the new server using OWA or Active Sync (Mobile device), it fails to work.  A couple of questions. One, how can I access the mailboxes on the new server while I migrate the remaining mailboxes from the exchange 2010 server? I'm trying to eliminate as much down time as possible for users that access their mailboxes from mobile devices. Two, I was thinking about migrating the mailboxes to two separate exchange 2013 servers. Is this even possible or a good practice, since I'm only able to access mailboxes (via OWA and Mobile Devices) that are currently on my exchange 2010 server? I know I can resolve these issues if I move them all at once (which will take a good weekend), and update my firewall to route OWA, SMTP traffic to the new server. I'm trying to avoid putting all my mailboxes in on one database and server. I understand exchange standard allow me to create 5 databases. But will the databases created for DAG use up the database mounts? I new to DAG, so I'll do my best to answer any additional questions. Thank you for your time.