Hellobee Boards

Yup totally ok. Just tell them you have medical liquids going through and separate them from the bag.

Yep all is ok. I flew with the dohm as well. No issues. Like peachy keen said if you think you are flying on a smaller prop plane, I keep a manual pump with me if I have to gate check. Just in case I get stuck on the Tarmac and need to pump.
Are you flying by yourself? If so, just walk yourself through security mentally prior. I had to practice getting LO into and out of our beco and taking the beco off while holding her without having somewhere to put her down. Folding the stroller one handed. Etc etc. it was fine. If you gate check the car seat you can ask at the gate if there are open seats. They might let you take the car seat on the plane.

Just out of curiosity, why don't you want to check the sound machine and video monitor? In my experience you have so much to juggle flying with a baby, you should check whatever you can. If you're worried they'll get broken just roll them in clothes.

@MrsADS: I carried on our white noise machine, video monitor and cameras, full Thermoses of milk, and a breast pump (and bags of frozen milk) before. The only thing that was of concern to TSA was the milk because it was more than 3 oz. of liquid. They just waved a little wand around it and that was it. No issues with the electronics at all.