Hello, my name is Sanjeev Mansotra. Can anyone help with the below questions, I’m new to this!
What is a common technique used in recording vocals to achieve a clear and polished sound?
What is a common technique used in mixing music to create depth and separation between different instruments?
Ducking the music with the vocal, (particularly where their frequencies coincide) … Auto Duck - Audacity Manual
I used to subscribe to Recording Magazine. They’ve got a Website with some good information. You might want to look for a book, which should be better (more organized) than the Internet. 
Of course the Internet has plenty of information, but it’s mostly useful if you need some help with something specific.
It’s all links in a chain and it starts with a good performance.
Then, you need a good microphone. Studios use directional Large Diaphragm Condenser mics for almost everything. It doesn’t have to be crazy-expensive, but it’s generally going to cost you between $100 and $200 USD (or more).
And, a decent audio interface, again usually $100 or more. One feature I’d look for is direct-hardware zero latency monitoring. If you monitor yourself through the computer there is always SOME latency (delay) and IMO, it better to avoid that altogether than to try to get the latency down to where it’s not noticeable.
As an alternative, there are mixers with USB double as audio interfaces. Most inexpensive USB mixers only put-out the stereo (or mono) mix so they aren’t good for multitracking. (Audacity isn’t great for multitracking either.)
There are some good studio-style USB “podcast mics”, which are super-handy and will save you some money, but they are somewhat limited. You can only record from one USB device at a time, and you can’t use a USB mic for live performance or with a mixer or audio interface.
The most difficult (and expensive) thing about a home studio is getting a good-quiet acoustic environment.
Again, it all starts with the arrangement and performance. When a band plays live it’s mostly up the band (or the band leader) to get a good overall sound. The “sound guy” plays a smaller part, mostly just trying to make sure all of the band members can be heard.
But when you’re mixing, you mostly use your ears to get a good balance between the instruments. And you may slightly fade-up or fade-down certain tracks during the song. You can use the Envelope Tool for that, and the trick is to fade-up and down with no sudden jumps in volume.
My “philosophy” is that a good recording doesn’t need any effects, but that’s usually not realistic…
Dynamic compression & limiting (both with make-up gain) are one of the “big 3” effects. Compression & limiting on the vocals can bring-up the loudness/intensity and help them to stand-out. (Limiting is a “fast-kind” of dynamic compression… Audacity has an excellent limiter.)
Vocals are the most important thing (if/when there are vocals) and they shouldn’t be buried in the mix or drown-out by an instrument.
A professional recording will usually have some compression on every track and then more compression/limiting on the mix during mastering.
Virtually all commercial recordings have compression. There may be a few classical & jazz recordings without it.
Compression/limiting during mastering is how you “win” The Loudness War. But, over-doing it kills the dynamic contrast, and IMO it makes music boring!
Equalization is another of the “big 3”. It’s mostly used as a “corrective effect” (to correct for microphone characteristics, etc.). It can also be used to “bring out” certain instruments or characteristics of certain instruments.
Reverb is also commonly used. It’s usually used subtly so you don’t really notice it but “something’s missing” if you take it out. (That’s a creative effect so it’s up to you).
One trick the pros us is to have a known-good reference recording in the same genre. It’s not to copy the sound, but to “keep your ears calibrated”. You can easily get carried away with effects and that can help.
And assuming you don’t have a great studio with great monitors, it helps to listen to your production on as many things as you can get your hands on… your headphones, or in-ears, your car stereo, etc. Pros do this too, but usually just as a last-check.
…And if you want to “get serious” about multitrack recording & mixing, you’ll probably want to step-up from Audacity to a Full DAW. They are designed from the ground-up for multitracking. It’s a big learning curve but they have “automation”, which is similar to the Envelope tool but easier to use (“easier” after you learn how). It will a master level control, which makes mixing easier, and you’ll have a master meter as well as meters for each track. You can also apply (or un-apply) different effects to different tracks as you are mixing.