Hi Courtney,
It sounds like you're using 'tables' as a means of structuring things? Tables have never been brilliantly responsive (Google it), thus changing themes will probably not solve the issue. Essential should have responsive images without any additional CSS.
File format will have no impact on responsiveness.
What functionality is missing from the 'Insert Moodle media' dialog?
Could you post a screen shot of the videos on the right hand side of the table please?
G