I assume this is for a Core Barbarian, not an unchained one?
Also, this would be better in the rule question forum. ;)
Anyway...
1. You get 4 rounds of rage at level 1 and 2 more for every additional level. That's 4 + 2*4 = 12 rounds at level 5. You also add your Con Modifier. So if you have Con 16, that would be another 3 rounds for a total of 15 per day. The Con bonus of your belt also counts for the number of rounds.
2. You get +4 strength. This increases your strength modifier by +2 and the modifier is added to all melee attacks and melee weapon damage. So rage increases both your attack roll and your damage by +2. If you use a two-handed weapon, you get 1.5 times your strength modifier to damage (but not attack). So for a two handed weapon, rage will increase the attack by +2 and the damage by +3.
3. Power attack lowers your attack by 1 and increases your damage by 2. While leveling, each time your base attack bonus, which is equal to your level, reaches a multiple of four, these numbers increase by one step. At level 4, the attack penalty becomes -2 and the damage bonus increases to +4. The next increase step would be at level 8 (-3 attack, +6 damage). Like the damage from strength, the bonus damage of power attack is increased by 50% when using a two-handed weapon. So at level 5, Power Attack would reduce your attack by -2 and increase your damage by +6 for a two-handed weapon.
4. With raging Vitality you get +6 Constitution in rage, increasing your Constitution modifier by +3. This increases both your current and your maximum HP by 3 points per level (15 points total at level 5). So if you have, let's say, 50 of 60 HP before rage, this would become 65 of 75 HP in rage.
The same is true when you end your rage. You will lose 3 HP per level from both your current and your maximum HP. Let's say you are at 5 of 75 HP in rage. When you end your rage, both numbers drop by 15, leaving your with -10 of 60 HP! That's why rage is always a risk, even though raging vitality makes your survival much more likely.
1) How do I work out my rage days? Does the con bonus include items? I have a belt that gives me +2 con for example.
Permanent (or semi-permanent) bonuses like that from a belt counts as your Con for all purposes. A temporary bonus, like drinking a Potion of Bear's Endurance, doesn't count.
When I rage I get +2 to attack is that damage or to hit? My strength increase contributes to the damage right?
Both. You increase strength. Strength goes to both hit and damage.
How does power attack work? We use average damage rolls so it makes it easy to calculate.
A 5th level barbarian has a base attack bonus (BAB) of +5. At that level, power attack gives you –2 to hit but +4 to damage. If you hold your weapon in two hands (and you should!), that damage increase is even higher, +6.
How does the hitpoints from raging work? Do they go first? I have raging vitality so I don't die! Cheers
Yeah, raging and hit points are confusing.
The extra hit points from rage aren't separate from your normal hit points.
The problem arises when you go into negative hp and fall unconscious.. You die when you reach negative hp equal to your Con. But a raging barbarian has additional Con, which mean they should die later, right? Wrong!
A barbarian ends raging when falling unconscious. Say your normal Con is 16. Then you get raging Con 20. Those extra 4 Con gives you 2 extra hp per level, so 10 extra at level 5.
When you end up at say –15 hp, you aren't dead. But you stop raging, so you loose that extra 4 Con - and those extra 10 hit points. So you effectively take an extra 10 damage and end up at –25. Dead!
Raging Vitality stops all that nonsense, provided your allies reach you in time (before you loose all your rage rounds) and can heal you.