The speed decreases before the altitude starts to rise, is that just because the data is approximate, or an indication of engine trouble (ice ingestion ?) ?
Coupled with the information that there may have been 2 tailstrikes on the takeoff run, it suggests that the crew were just not getting the lift they needed and were running out of runway, but not wanting to overrun if they could "get away with it" and depart without incident.
The graphed speeds suggest that it should have been able to fly (150+kt at one point). The airport is fairly elevated, 2234 ft, but if there was icing conditions then the penalty of that elevation is mitigated due to denser air, but they'd still have needed extra speed even so (I don't have any numbers).
The drop in speed could be due to several factors, engine-related, or perhaps just position error on the pitots if the aircraft slewed enough - or if it was just back in contact with the ground and/or slewing, in which case the drop would look catastrophic.
The two tailstrikes - or at least a nose-high attitude enough to cause one - may have bled off some speed and a last-ditch attempt to get airborne (maybe the second tailstrike) was enough to stall the aircraft, starboard wing first, making it settle back onto the ground soon after getting briefly airborne. The drag of starboard wing contact sets up a ground-loop and around it goes into the building. If there's a small berm or wall at the airfield boundary that would also factor in to the aircraft's final position.
The initial word on the engine conditions will be material ingested, I would think, at least, pending any data from the recorders.
A decrease in speed before a registered climb might just be the nature of the data, if speed is registered far more accurately or quickly than altitude changes. A lot happened in a very short time, which I think could exaggerate any differences in how the data is gathered. Certainly in all the aircraft I have flown (light GA), the altimeter was always a lot less responsive than the VSI, it lagged, so altitude data might be less trustworthy except in a general sense.
So in answer I think the altitude data is more approximate than the speed data, and the possibility of engine problems can't be ruled out as a factor in the aircraft struggling to get airborne and tailstriking twice. The fact that it notionally makes flying speed and doesn't get airborne might be a field elevation factor, or icing, or both.
If field elevation shouldn't be a problem, it may be that icing made it one. Factors lining up. Maybe I'm overthinking it.
Your mention of "ice ingestion" is interesting, since if the wings were iced up, I can't help wondering whether lift at rotation would be enough to pull ice off the upper surface and into the intakes (more likely if ice is in small patches and fairly inboard). It probably wouldn't be enough to damage the engines, but may factor in as a brief loss of engine power? Perhaps it depends on what kind of ice was there, rime ice or sheet, and that would depend on the night conditions, clear or precip, I would guess.
A propos of another conversation going on here... I tend never to fret about "it could have been me". The reason being that we never hear all
the news about everywhere
we travel. If we did, we'd never get out from under the duvet. I joke with my wife sometimes about how we'd never have met if I'd been on the 14th Street Bridge in DC 18 months after I'd last been there. Everywhere we go, even just down the road to buy something, we're "running the numbers" of probability whether we like it or not. We can either nurse a neurosis about it or just get on with life and accept that fate will do what it does, without favouritism or malice. I'm reminded of Samantha Smith, the girl that tried to bring a rapprochement between the USA and the USSR decades ago, scared as she was of nuclear conflict. As a result of her outspoken stance she gained a measure of celebrity, becoming a "goodwill ambassador", TV appearances etc, and she ended up travelling more - only to die in a plane crash at the age of 13. I'm not sure there's any point in trying to second-guess fate. Sometimes it's our fears that put us in harm's way.