I'm taking a trip with my Sony EA 50. I wondered what the issues have been for everyone else going through airport security, carry on bag, batteries, etc.

I was going to find a small carry-on bag just for the camera, mic, and lens(s), and check all my other stuff.

I do it all the time.
Actually no issues at all. Be nice.

Haven't done it for a while but honestly, I've never really had a problem traveling with my camera(s). I put camera, batteries, audio all in the carry on bag, chargers, lights (small LEDs) in checked bags. I had one TSA agent start talking to me about the gear but only because he was a "budding" vid guy.
You should be able to get the 50 and the ancillary gear in a Portabrace type bag that would go in the overhead without a problem.

If you search on "lithium Ion airline regulations", you'll find information saying that Li-On batteries need to be carried on and not checked. Further, you should have the batteries inserted in the device or cover the contacts with original packaging or insulating tape.

I use gaff tape which stores nicely on the battery when I am at the destination and is ready for the return trip.

There was no problem taking my EA50 between Sweden and Germany...