MacBook – Is MBP Pro 15” Retina fan noise reduced noticeably

Fan speeds are related to the temperature of your laptop. If you're just interested in monitoring the temps, iStat Menus ($16) has an excellent temperature monitor that sits in your menu bar and can track any of the dozen temperature sensors built into your MBP.

There are a few apps which purport to allow you to control your Apple laptop fan speeds.

EDIT: Updated Aug 2018

• Macs Fan Control -- $15, last updated Mar 2018
• smcFanControl -- Free, last updated Oct 2016, many users report that they can set fan speeds high, but not low

I've found that the best solution to keeping my computer cool and the fans off, even when really tasking the processor, is to put it on a little stand to allow plenty of airflow underneath. The one I swear by is a Podium Pad from 2004 which was discontinued long ago -- but there are many alternatives. If you keep your laptop on your lap, almost any simple lap desk can help a lot, keeping the computer on a firm surface to let the fans do their work without smothering them with fabric/skin. There are also active cooling pads with fans in them, some of which are very well-reviewed.

Finally, I'm not sure what you're recording, but you could try using a directional USB microphone to eliminate extraneous noise from your recording environment. There are many excellent options on Amazon for under $100 (be sure it is Mac-compatible before purchasing).

I can tell you, this isn't normal.

You shouldn't hear the hard drive very much at all, and only a little chatter when you're using it extensively.

Since you've clearly established that it's a hardware problem (because pressure fixes it), you should probably try to get it fixed. Rather than open the machine and do it yourself (violating your warranty), you should get Apple to fix it.
Since your computer is pretty new, it should definitely be a free repair.

You can take it to the Apple Store and tell Apple what happens. They'll take it and do some tests, then replace the drive (or whatever part they think needs it).

Make sure you back up all your data first; you won't get your old drive back.