How would Lucius go about trying to brainwash Harry? Would he involve others to help him do this?
Yes, I believe he would involve Narcissa and Bellatrix. Or the other Death-Eaters.
How power hungry is Lucius?
He does want power, but I don't think he would want too much of it so he can't control it.
We all know Lucius is heartless and cruel, but would he actually banish his own son? (Draco)
No, he loves his son very much. He would definitely use him, but never to banish him.
Does Lucius work alone or with others?
With others. If something goes wrong, he wouldn't like to take the blame. He's selfish that way.
I have a few questions about Lucius and the Malfoy family...
How do you think his relationship with his family of birth is? Does he have in any brothers or sisters in your opinion? In my story he is an only child. His parents are both obviously pureblood fanatics, but here, his mother is the one who wields the power in his house. She constantly ridicules her husband, and resorts to attacking Abraxas with a wand to get her way. Abraxas resents her for this and thinks she's a disgrace to the House of Malfoy, and tells her that. Their marriage was completely loveless, but out of duty. She knows the Dark Arts, but isn't very "subtle" as Lucius is, and as a result has had run-ins with the Ministry on several occasions, at which point she simply would just tell them to leave her alone because she's a pureblood and she'll do whatever she wants; usually she got away with it because she was very good at dueling, and the Ministry was somewhat weak in those days. Lucius's mother doesn't abuse him but pays practically no attention to him. He hates her. Do you think is plausible?
Also what happened to Lucius's parents? This is really confusing me, because it seems pretty clear that Malfoy Manor is an ancestral posession, but Grandpa and Grandma Malfoy don't live there. Did they die really young, or just move somewhere else giving Lucius the house?
With regard to their deaths, we know Abraxas is dead by Half-Blood Prince because Draco mentions him to Slughorn, and Slughorn says he was sorry to hear he'd died. I think he mentions dragon pox 'at his age', so I assume he wasn't young. The 'sorry to hear he'd died' part makes me think that it had happened recently-ish, within the last four or five years at the latest, and regards to his age, considering that Slughorn knew him, Abraxas could have been around the same age.
I'd assume that Grandma Malfoy was also dead by the time Deathy Hallows happened. She's not mentioned in that book and I think she would have been, if only in passing, if she was alive and lived in the house. She could have been living elsewhere, of course, but her absence makes me think she's dead as well. With regards to the house, manor houses often have farms and cottages on their land, as well as a lodge, perhaps during the last years of their lives, Lucius' parents retired to something like that, leaving the house completely in Lucius' hands. I'd hazard a guess that they lived there with Lucius at some stage, though, and may well have stayed until they died.
With brothers and sisters, I'm inclined to think Lucius is the eldest because he's inherited the house. We also never hear of any other family with the name Malfoy, so either Lucius was an only child, or his other siblings were girls who married into different families and therefore don't have the name Malfoy.
Regarding your characterisation of his mother, I think you have to think about how her behaviour would impact on Lucius. Experiences in childhood influence who somebody becomes in later life. You mention that his mother attacks his father and that their marriage was loveless. How would this affect his relationship with Narcissa? Death Eaters and everything aside, they do seem to love each other, and I think that often when children see one parent being beaten by the other, it makes them more inclined to domestic violence when they're older. How has Lucius' parents relationship influenced him?
I hope this helps.
Thanks, that kind of helps...I'm not entirely sure what characterization of the Malfoy parents I'm going with...I can probably make it work a different way, and now that I think about it that would be better for my plot...