1.) How does Mephala differ from Azura, if her webspinning is indeed associated with the threads of fate and time?
Is Azura associated with fate and time? I know she's involved herself in these things with the Nerevarine, but I don't think she's ever been directly associated with them. I'm more inclined to associate her with transitions, as dusk, dawn and twilight implies, and with a mysterious association with Nirn and the female principle that's yet to be fully explained.
2.) How does Mephala differ from Boethia, if she is indeed associated with assassination, in the sense of plotting and overthrow?
Mephala is a meddling schemer, but that's not her sphere, even if it is in her nature. Her sphere is actually unknown; "http://www.imperial-library.info/mwbooks/book_of_daedra.shtml; known by the names Webspinner, Spinner, and Spider; whose only consistent theme seems to be interference in the affairs of mortals for her amusemant." (I'm aware the document "Vivec and Mephala" says differently, but I imagine the description of Mephala as the demon of murder, six, and secrets is more generalising of her nature, not her sphere.) Astion's point is a good one. Her actual nature is ambiguous, her actions shadowy, her motives unknown. Boethiah, however, seems quite solidly associated either with http://www.imperial-library.info/dfbooks/b080_azura.shtml or with http://www.imperial-library.info/obscure_text/census_daedra.shtml. Almalexia, who is associated with Boethiah is a warrior, though she plots and schemes to get you into her confidence. This is in contrast to Vivec, who is also a warrior, but who, like his Anticiation Mephala, is similarly shady to the point of being incomprehensible.
I'm aware this doesn't really answer your question, but it's the best I got, and Astion already said most of what I wanted to say on the topic. I might venture to say that while Boethiah is the Prince of Plots, Mephala is the Prince of Intrigues, but I'm not sure how accurate that would be.
3.) Is Mephala caring of her followers? If no, then why worship her. If yes, in what sense or actions perhaps, would she show it?
I'm not sure that the only reason someone would worship a god would be if they expect to get something from it. Like any religion, the act of worship can be its own reward, as would the study of what that particular deity signifies to you.
4.) How would a worshipper, High Priestess in this case relate her/him to a beggining follower?
I'd imagine she'd draw them in gradually, not necessarily by appealing directly, but by laying a series of scenarios or obstacles in their path that either convinces or scares them into embracing Mephala. It doesn't have to be as dramatic as that. It really depends on the character. Through fashion, through prostitution, through staged chance meetings that reaffirm faith. Maybe the high priestess knows secrets about the character known to no other. Play with the webspinner, secrets, six and murder attributes.
However, Mephala's has influence over many aspects of life, and is bound to have several sub-cults, which do not necessarily have to be about murder. sixuality, secrets and fashion are also in her sphere.
Transvestite killer prosttutes can cover all three, right?