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- Will anything happen to me or my belongings during those last two weeks in the building?
Most probably yes if they think they are going to do a runner without paying the rent. Most landlords/agents can be flexible when it suits them but this women sounds like she would make your life hell on earth.

- Do I say "I am not paying the rent" or just make excuses we both know are not true?
NEVER say you are not paying the rent!! They'll have you and/or your stuff out on the street before you can blink. Make excuses that your employer is having some difficulty with their bank or something (maybe they 'accidentally' paid it into the wrong account and you are waiting for them to make an emergency payment or... something....
You paid a deposit so they might be happy to wait.

- If they threaten me, are threats to be taken seriously?
Yes. Sometimes this becomes a physical confrontation especially if they think they are losing face. The best case scenario you should expect is you being locked out.

- Will I be stopped at the border if I leave the country?
Not unless they know someone at immigration.

- Will I be blacklisted if I return?
Highly doubtful.

Thanks, ScriptShack, for your thoughtful response. I got lucky, or fierce, or something and the Real Estate Management Woman From Hell caved under pressure from the landlord. I have to think - from a suggestion someone made online in this thread or elsewhere - that using the word "police" every once in a while focused on their attention of the benefit/risk equation. I got every penny back and didn't have to pay a speck more rent.

Reads almost, as you know. from who you did rent

As far as I know, there's only one major real estate management company operating in Tay Ho. New signs. Front walls. Black lettering.

I've decided that the security deposit issue is just not worth the hassle. You invariably move into a place that's seen better days and even when you document every nook and cranny on the lease signing day, they give you a hard time.

I'm now a convert to airbnb. Places are much nicer, landlords are much nicer, airbnb as an arbitrator is much nicer, even monthly prices are much nicer. Look for young owners with only a few properties with a healthy bank of immaculate reviews.

So long, real estate management companies! So long, entrapping leases and hostage security deposits! Free at last.

Glad it worked out.
My large, nice apt building also had a change of management, but not as drastic changes, though a few less people around and not cleaned  daily like before.
I also moved out two months early for my own reasons and never really dealt with the management people, but with the owner directly, since that was the person we signed the lease with.
I thought there would be an issue with me leaving early, but turned out to be no issue at all. YMMV

thanks for the Air bnb advice, good to know for anyone thinking of medium or long tern living.