Slave
Dunmer keep slaves. That's just a truth and nothing to reconsider or discuss. The Ebonheart Pact might have forbidden to enslave Pact races, but that just means there are more Khajiit and Breton slaves around... Well, or other non-Pact races.
What am I doing all day?
Whatever your Masters expect you to do. You might have a general occupation though. Most slaves are used for everyday work such as cleaning the chambers, carrying around goods or feeding the guars. Slaves in Heimlyn Keep that actually work there might be familiar with the staff there and could be subordinated of any of these.
My powerlevel
Most slaves have a very low powerlevel, though there might be a few ones, especially slaves used as some kind of bodyguard or for special jobs, that exceed this standard.
Where is my place in the Great House Telvanni?
You are a slave. Lowest of the low, considered an object by many of the Wizards.
My agenda
If there is hope left inside of your character to become something more than a slave, you should hide it very well.
Additional information
Playing a slave might not be as easy as it sounds. It highly depends what kind of slave you want to play, but your character's Masters will adress him/her and he/she will likely have a fair share of humiliation... Since we had an incident concerning this matter, I want to be clear on one point: slave gameplay isn't in any way considered to have bdsm content.