First time flying? Liquid rule and what to do after arriving at the airport?

It's my first time flying so I've been trying to watch some videos on what not to do while going through security and in a lot of the videos liquids are shown in clear plastic bottles. My makeup bottles are glass but are only 1 oz so I had assumed that it was okay to just leave them in their original packaging and put them in a plastic bag since they're less than 3 oz but should I put them in plastic bottles just to be safe?

Scoping through various websites (including the airline's) on TSA regulations doesn't specify anything pertaining to glass makeup bottles. I'm assuming that the liquid rule only applies for liquids that are originally in containers larger than 3 oz but I would rather be safe than sorry.

Also tips for what to do upon arriving at the airport would be super helpful because it's holiday season and I know the airport will be very busy so anything to help avoid headache is appreciated. Like checking in, what to do after going through security, etc.

Problem flying with a samourai sword?

In 1999, I flew from UK to Portugal with a samourai sword (value: $15,000! - and I have the skills to use it).
It was taken (with as mile) to the flight deck, and returned to me in Faro airport.
As a pilot, I often flew with TAP, in the jump seat.
Since 9-11, things have changed…
Now… How can I air travel to, say, China, Japan, or even UK, with that weapon?

Can you use luggage in public spaces?

Like is it socially acceptable to use luggage when you re outside of an airport and not traveling? I just don't wanna look like a freak when I carry my stuff around in a duffel bag in public.