If a spell or item affects an attribute by 8 for 10 seconds, does the effect multiply per second like a damage health effect or does it stay constant at 8 for 10 seconds?

Quite sure it is a constant for both.

http://www.uesp.net/wiki/Oblivion:Drain#Drain

Drain does not multiply over time. If you cast 10 Drain Health for 10 seconds on a target with 100 Health, the target will have 90 Health for 10 seconds after which it returns to having 100 Health.

For Absorb it depends. Absorb Attribute and Absorb Skill work like a combination of Drain (target) and Fortify (self). Absorb Fatigue, Absorb Health, and Absorb Magicka on the other hand work like a combination of Damage (target) and Restore (self).

Thank you for the information.