I've been dabbling in writing music myself for some time (since 2000), but I haven't really ventured into the realm of film scores until the last couple of years. So, for that I'd have to say I'm a bit of a beginner. :-)
I've never had formal training in composition, just a bit of music theory back in middle school, and I've performed in music in some fashion or another since I was old enough to make my voice heard. So, while I either don't know, or don't remember, a lot of the technical jargon that goes with it, I do know some and have experience putting notes together. Honestly, it's amazing what you can learn from simply listening to a few successful composers.
To move on to the topic, please bear with me as I'm sure my answers will sound a bit... amateur.
1. In my limited experience, it seems a number of directors, especially newer ones with low(er) budgets are more willing to receive computer-produced music rather than a full live score. Of course, the downside to that is that while it eases the testy budgets of the director, it puts quite a bit more financial strain on the composer, due to pressure to input higher-quality productions. Which leads to my second question...
2. So far, my experience is also limited in this department. My most-used programs (since I submit my work electronically) are FL Studio and Finale (2008). For the project I'm working on right now, I've been writing the music in Finale, then exporting it to .wav and importing it to FL Studio to make any final adjustments and export to Mp3. The nice thing about FL Studio is that you have a decent amount of flexibility with its video player in timing the sections of the piece to the cues. Plus, if I want to enhance various sounds (such as drums/perc and others) to bring them out better than Finale can, it works well with that.
So far, Finale has been great for writing music. My only gripe is that the Mac version has a bug in it that won't allow you to change the reverb settings. But I do have to say that the Human Playback function is really nice. I use to write my orchestral pieces using FL Studio, but the process is extremely tedious, since you have to manually adjust the tones and volumes and tempos to make it sound how you want.
3. As for favorite styles, can't really say too well at this point. I do tend to write with baroque influence, especially with brass sections of pieces. Hey, I played trumpet for 11 years, what can I say? :-)
I also tend to take influence from Tchaikovsky, Copeland, Sibelius, and maybe a little John Williams (kind of hard not to, his music's everywhere http://studentfilmmakers.network/file/smile/wink.gif" mce_src="http://studentfilmmakers.network/file/smile/wink.gif" alt="" phpfox="image-protect"> ). I also really admire Jeremy Soule's work (game sound track composer for those who don't know), so I take a few cues from him as well.