Beck's First Flight (tell us how to do it)

Guys we're going to NYC on Friday!

I found out I was pregnant the day after we got back from this trip last year, and this year Beck is coming with us!  We're super excited and also terribly unsure of ourselves because duh, first time parents and a 4 month old in a big city. We aren't scared of cities, which is a good thing.  

So far, we know that we aren't taking a car seat (because we hate safety, obviously), we are taking a stroller, the Ergo baby, and that's...as far as we've gotten.  

Funny story about the flight, when I booked our tickets there was nowhere to say WE HAVE A BEBE, so I just...thought you show up with the kid?  I don't know, I'm dumb.  As my mom says, but how will they know she isn't muslim? Anyway, I got to thinking about this, called Delta, and they were all "babies can only fly on the right side of the plane, and your seats are on the left side.  It will be $19 per ticket to move you."  Um, no, no it will not.  I told them that that made no sense, and SURPRISE they moved us to the right for free.  Because clearly that is a dumb policy.  But they did it, which is all that matters.  

Here are some questions I have:

• Besides nursing as much as possible on takeoff and landing, flight tips?  We have direct flights going and returning, thank heavens. 
• We are considering using a sitter service in the hotel for a few hours at some point.  Chime has been recommended to us, and looks super legit.  But then also omg leaving our baby with a stranger in a hotel.  Thoughts besides "I wouldn't do that, you're a bad mother?"  Other services you've heard of or used?  
• TSA or other considerations?  I AM taking some pumped milk and want to be darn sure I can get on the plane with it.  Can I just take it in 3 ounce portions in a large ziploc bag like toiletries to avoid any confusion/issues with moronic workers?  What about ice packs?  We are flying Delta, if that helps you add more specific advice.  
• Beck's packing list includes a few toys, extra clothes, diapers, bottles, wipes, extra pacis.  I'm trying to go super minimal but also have everything she needs.  

Ok, tell me your wisdom.  Be gentle with us, we're new!