As far as AC bonus for Tumble goes, it uses only the raw skill ranks invested. There are no modifiers/penalties applied, and it caps at +4 AC bonus with 20 ranks.
Tumble checks like when moving around in combat or for "acrobatics"-style activities, by contrast, will still apply any bonuses/penalties from attributes, gear, spells, etc.
Your Parry AC bonus is easier to calculate if you look at it from two steps:
1) Determine your Max Possible AC Bonus from Parry due to ACP: (30 - ACP)/5, round down
So if you were wearing studded leather (-1) and using a large shield (-6), (30-7)/5, rounded down =
+4.
2) Determine your actual Parry score AC bonus: (Modified Parry Skill/5), round down, capped at +6.
So if your modified Parry skill was 27, your AC bonus could potentially be
+53) Use the least value of #1 or #2. In the above example, even with a Parry of 27, your AC Parry bonus would be +4, since it is the lesser of the two values.
As Vetala said, though, the Bonetti/Thibault/Agrippa feat chain will add to the displayed value when you equip a melee weapon in the main hand:
With those feats it's quite possible to make that display go past +6 which can make the calculation look confusing: