Rewards, at the Reward trader south of Daemoneim.
you get it from dungeoneering for 34k or 44k tokens
You can only get dungeoneering tokens by getting experience in dungeoneering - that is, by completing dungeons, alone, or in teams of up to 5 people.
If by Gravity Shortbow you mean the Gravite Shortbow, it's a reward bought from the Reward trader for 40,000 Dungeoneering tokens outside of Dungeoneering. It can't be brought into the dungeons and isn't an item in the dungeons.
The best longsword, according to the runescape wikia, is the chaotic longsword. The chaotic longsword is obtained via the dungeoneering activity. It costs 200,000 tokens and if completely uncharged will cost 2 million coins or 200,000 coins and 20,000 tokens to recharge to 100%.
You need 40,000 Dungeoneering tokens, so you need to get about 400,000 Dungeoneering experience. I couldn't find any reference on how much experience you typically get per hour, and I don't have enough experience myself yet.
The best way to get tokens in dungeoneering is to get as much experience as you can on every dungeoneering floor. You get tokens from 10% of your total experience. For example, if you get 5,839 XP you will receive 583 tokens. Total experience depends on the floor XP and prestige. So make sure you raid the floors only once. After you've raided all available floors, reset your progress. You will also receive more XP when you raid floors in a party with other players. If you do raid in a party do not be a Leecher! A leecher is someone who just stand there and doesn't help the party.
from the dunginering tutor
Yes.
drink the antidote
Fractite hatchets, and other fractite items, are items used specifically in Dungeoneering.
The deepest level floor available to non-member RuneScape players is floor 35. Floor 35 can be accessed by players after reaching level 69 Dungeoneering (about 650,000 experience in Dungeoneering).
Red and Gold band.