Is it possible to change the text in the "Request Membership" dialog box?

Yes, these can be modified. Click Pencil Icon > Administration > Interface > Widget Studio. In the Viewing drop-down scroll down and select 'Request Group Membership Modal' under Extensions, then select Resources. From there you will have access to modify the text. 

Yes, these can be modified. Click Pencil Icon > Administration > Interface > Widget Studio. In the Viewing drop-down scroll down and select 'Request Group Membership Modal' under Extensions, then select Resources. From there you will have access to modify the text.