Please help me making realistic (dry & crisp) piano sound

You should try the built-in demos of the YC5 or U4 and download the free instrument packs (if you haven't already--the Pleyel, Erard, & Bechstein specifically).

Those instruments will likely get you closer to the sound you want immediately and you can configure from there.  While the B is a smaller scaling than the D, it isn't that close to what (by appearance) seems to be a ~70s 6' Yamaha, which are among the most responsive pianos I've played--great for something like Mendelssohn's music (though for my tastes they're terrible for just about anything else, I only use them when I'm doing one that really, really needs their exact "personality").  They typically have minimal ringing time (horrible for Old-Russian-School pianists like myself whose pedal philosophy is "set-and-forget-it"), higher-than-average soundboard impedance, fast hammers, and faster repetitions than I usually find in most pianos (though that can sometimes be as much or more of a regulation consideration than an action-design one).

Yes, upgrading to Standard will be a dramatic improvement as far as configurability; however, it might not need to be your immediate first step.  Also, much fo the example video sound is related to EQ (due to the microphone in question have profound axial character--as the bass notes are virtually inaudible while the mid treble is extremely present): giving it something of a "radio" EQ sound.  You can also try Standard for free, with some notes turned off.  Spend an hour or so experimenting in Standard and see if you're getting better results or not.  I believe you'd also get another instrument pack with the upgrade to Standard.  You'll keep all of your settings and experiments if you do choose upgrade, which is a nice bonus--as it means the time wouldn't be wasted if you went that route.

Also, a word of caution: avoid conflating "sound" with "experience" as you describe wanting "very crisp...sound with instant hammer responses" as much of that likely has to do with your MIDI interface/keyboard and sound card latency settings/driver configuration, etc. and your personal playing technique when using your specific equipment than it does with the actual piano sound settings within PTQ.  You can use MIDI scans of piano rolls as control subjects (when doing a high quality audio export) to help isolate if the sound issues are more related to PTQ itself or the rest of your equipment chain.