Feel free to add your ownThese aren’t in any particular order and whilst some may be obvious – to someone, they won’t be, so I’m saying them anyway.
I’m also unsure if the listings for items / powers are requirements or bonuses. I’ve listed them as bonuses here, but they may be required stats.

Fleeing from a PvP battle counts as a loss.
Your winning streak is reliant upon beating those who challenge you as well as your own initiated fights.
All stat points raise your stats by 1 except for HP which raises it by 2 per point.
PvP fights require 2 stamina.
Stamina regens at 1/5min Mana regens each turn in battle only, Energy is 1/3min
Using items in a battle takes up your turn.

Accuracy – Chance of landing a hit in battle
Speed – Chance of attacking first in a turn
Dodge – Chance of dodging enemy attacks
HP – Take more hits during a battle
MP – Use more amazing powers in battle

Night Stick – 15 Damage – Acc +11, Spd +1, Def +1 COST: $50 UNLOCK L4
Intratec KG-9 – 31 Damage – Acc +24, Spd +2, Def +2 COST: 19 GEMS UNLOCK L5
Katana – 42 Damage – Acc +33, Spd +3, Def +3 COST: 39 GEMS
Zweihander – 49 Damage – Acc +41, Spd +5, Def +5 COST: 69 GEMS
Claymore – 56 Damage – Acc +48, Spd +7, Def +7 COST: 99 GEMS
Flintlock Pistol – 37 Damage – Acc +31, Spd +2, Def +2 COST: 29 GEMS UNLOCK L5
Butterfly Knife – 12 Damage – Acc +10, Spd +1, Def +1 COST: $30
Mallet – 19 Damage – Acc +11, Spd +2, Def +1 COST: $70
.38 Special – 26 Damage – Acc +12, Spd +1, Def +1 COST: $80
Taser – 33 Damage – Acc +13, Spd +2, Def +2 COST $190 UNLOCK 13

Brief Invisibility – Acc +4, Spd +4, Def +9 COST: 20 GEMS
Camouflage – Acc +1, Spd +1, Def +6 COST: $50 UNLOCK L5
Armored Jacker – Acc +0, Spd +0, Def +5 COST: $20 UNLOCK L3
Kevlar Plating – Acc +2, Spd +2, Def +8 COST $200 UNLOCK L11

Criminal Hogtie – Acc +3, Spd +9, Def +3 COST $140
Heavyweight Lifting – Acc +13, Spd +4, Def +2 COST $130
Catch Everything – Acc +3, Spd +6, Def +2 COST $90 UNLOCK L5
Enemy Toss – Acc +7, Spd +2, Def +2 COST $80 UNLOCK L3
X-Ray Vision – Acc +18, Spd +5, Def +3 COST $170 UNLOCK L12
Gigantic Leaps Acc +12, Spd +8, Def +4 COST $180 UNLOCK 13

A power must be equipped to upgrade it.

10 min+40 dollars from level 1 to 2
20 min + 60 dollars from 2 to 3

Ice Spikes 4MP UNLOCK L1
L1 – 16 Damage – Acc +17, Spd +3, Def +2
L2 – 19 Damage – Acc +20, Spd +6, Def +5

Electrocute 4MP UNLOCK L1
L1 – 16 Damage – Acc +17, Spd +3, Def +2
L2 – 19 Damage – Acc +20, Spd +6, Def +5
L3 – 24 Damage – Acc +25, Spd +11, Def +10

Boulder 4MP UNLOCK L1
L1 – 16 Damage – Acc +17, Spd +3, Def +2
L2 – 19 Damage – Acc +17, Spd +3, Def +2

Fire Blast UNLOCK L5
L1 – 27 Damage – Acc +17, Spd +3, Def +2
L4 – 42 Damage – Acc +32, Spd +18, Def +17

Tidal Wave
L2 – 34 Damage – Acc +21, Spd +4, Def +3

Lose $307 in 10v10 fight with Crit kill shot

Level up only fills energy.
Fights provide extra exp or money in quests – $8 or 2xp for killing 1 person. – 6 xp for killing 2. = of the level 20 variety only atm.

L2 22xp SP 5 EN 5
L3 xp SP 5 EN 5
L4 108xp SP 5 EN 5
L5 247xp

Fire Blast and Tidal wave – 8 MP activation cost
Level 7 Electrocute – 64 DMG
Level 8 Electrocute – 79 DMG
Level 4 Fire Blast – 42 DMG
Level 1 Instant Healing – 101 HP

lvl 3 tidal wave – 49 damage
lvl 4 tidal wave – 55 damage
lvl 7 boulder – 37 damage
lvl 5 fire blast – 44 damage
lvl 6 fire blast – 50 damage
lvl 6 electrocute – 33 damage
lvl 7 ice spikes – 37 damage