Do you think she's in love with Voldemort, or is it just the power?
I think that Bellatrix loves Voldemort, particularly the power that he holds and the power that she gains by standing with him, but she isn't in love with him. She appears to have romantic feelings for him, true, but even assuming he had feelings for her as well, they could never form a deep relationship, or even anything remotely amounting to true love. Feelings based entirely on power, which I think hers are, are not equivalent to being "in love". When that power inevitably falls, as all power does in time, there is nothing else left.
The best comparison that I can think of is from another fandom Death Note (by Tsugumi Ohba and Takeshi Obata). This is a wonderful manga/anime that I hope some of you are familiar with; if you aren't , I hope my comparison still makes sense SPOILERS for the series follow so if you ever plan on getting into Death Note, don't read (highlight to read): In Death Note, the main character is a guy (by the name of Light Yagami) who takes it upon himself to murder all the world's criminals, thereby ridding the world of evil. Another man later helps Light, basically serving him the way the Death Eaters serve Voldemort. (This other man's name is Teru Mikami.) Mikami reveres Light, much as Bellatrix reveres Voldemort. He pledges his loyalty to Light, even referring to him as "God" or "my Lord". Both are pretty twisted characters, murdering without a second thought "for the greater good". (This all sounds kinda familiar, huh?) But in the end, when all is said and done and Light's power is truly gone, Light no longer holds any interest for Mikami. And Mikami then cries, "What is this? Look at what you've gotten me into! You're no God, you're just scum!" I think that if Voldemort's end had gone differently, so that Bellatrix had been forced to merely watch as her master met his end - rather than acting on her in-the-moment rage as she did - things in the Harry Potter universe might have gone differently. With Voldemort's power - the only thing of interest to Bellatrix - gone, she would have denied her connection to Voldemort as much as possible. She would have renounced her "love" to save her own skin.
Would she give her life for Voldemort, or is it more important?
I think she would give her life for Voldemort as a spur-of-the-moment thing. Acting on rage and "battle fever" so to speak, she would be caught up in the adrenaline rush and do anything to save him. If by some chance she only learned of Voldemort's death after the fact, would she still retain her loyalty to him? I think not. As I said before, with the power gone and nothing left for her to gain, I think she would see no point.
How deep do you think her feelings run?
In general, I think her feelings definitely run deep. She is not a flat character by any means. I think that she perhaps hides most of her true feelings, locking them deep inside her. I picture her as one of those who is afraid of showing "weakness", especially through strong emotions (outside of hate and vengefulness, that is ).