To answer your first question:
Think of your mix as a 3 Dimensional space and not only as a 2D stereo plain. One of the most basic principles of psychoacoustics is that bright sounds ie. high frequencies (hit hats) sound closer where as dull or bass frequencies (kick drum, bass guitar) sound further away. Therefore, if you want to make your background vocals "take a step back" from the main vocals, you should try eqing some of the hi frequencies out of them. Also, as mentioned, reverb is a good effect to use because it tends to dull the hi frequencies of the sound it is applied to.
second question:
The first thing you have to consider when doing home vocal recordings is getting a descent condensor microphone. The best mic for the money is
a Rode NT1A. The next consideration is sound proofing. Don't worry too much about this now, just make sure you are happy that the background noise level is as low as possible.
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A few tips on recording vocals. All microphones experience what is known as "proximity effect." This means that the closer you are to the mic, the more bass frequencies will come through on the recording. Keep this in mind when doing a take.
EQ- This is another topic that can't be explained in detail, but there are a few tricks I can share. The vocals fit usually between 100hz to 15khz but are strong between 1khz-5khz in the frequency spectrum. We all want nice clear high's on our vocals but find that when we boost the high-end we receive sibilance on our "SS's" and our " SH's" These sibilant frequencies are usually in the 6khz-11khz ranges. Try boosting 16-20Khz by about 4-8db and it will open your vocals up without increasing the sibilance. If sibilance is still there, you can boost closer to 20khz, or you can try finding the frequency and reduce it using a small Q by 3db or more. A deesser also can work in this situation if you have one at your disposal. To try to achieve this you can also use what is called subtractive Eq, which is instead of boosting the high end we subtract or remove frequencies in the low mid range. I find depending on the voice, a muddy type sound is there due to a boost in the 500-700hz range, be careful not to remove too much in this frequency range or else your vocal will sound light and will not sound full. If you must remove these frequencies more than 5-6db boost your the low end of the vocal at around 150hz-250hz to give the effect of bottom end on the vocal sound.
One more trick I would like to bring to the table is the 2Khz mystery. When your mixing your track and having a difficult time placing the vocal. Try boosting 2khz on the vocal track by maybe 2db-3db at the absolute most!!! It will help if the vocal is getting lost in the mix. NOTE. If you boost it too much the vocal will sound like an AM radio.
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hope this helps