Outlook isn't showing older messages
This is probably because your local mailbox size (Outlook PST file) isn't large enough to store all your messages locally. GSSMO stores the most recent messages locally (up to 1 GB by default). It stores the rest (up to 25 GB) in the cloud, where it's accessible from the Gmail interface. If you want more messages stored locally, you can increase your Mailbox size limit, say, to 2 GB. However, this isn't normally recommended as it can have an adverse effect on performance.