Here are some back of the envelope type figures for the question you asked. They are for a BBJ2 so they are relevant for an -800 with winglets.
The figures are from the manual and not the BLT if you want the BLT figures then you will need to give me either the ICAO aor IATA three/four letter code and I will see if it's in our database.
From the manuals:- 2000' Pressure altitude, 20C QNH 1018, you will be field limited (assuming no close in obstacles), Flaps 5, engines 27.3K RWY req.d approx. 6600'
V speeds wet V1 127KIAS, VR 137KIAS, V2 148 KIAS.
For your Fuel question;- again from the books.
1700nm 40 kt H/W =1856 air miles. Which requires 18500lbs of fuel and flight time is approx. 0405hrs
Alt 250nm H/W -20 kts = 260 airmiles. Worst case scenario at 10,000'=5400lbs and takes 00:51 mins. More realistic FL280 = 3500lbs and 00:46 mins.
NBAA fuel reqd. taxi 500lbs, trip 18500lbs, Alternate 5400lbs, 00:45 mins reserve (@MLW and 1500') 3850 lbs Total 28250 lbs.
Hope that helps.
All usual caveats apply!