I am an 'adult male human' and can sing from A2 to G4 comfortably. It would be great if I can sing up to a whole octave below this. I am in no hurry and am willing to expend time and effort. I just want to know what are the techniques and what amount of work would be involved. Also, I would like to know what is the difference between a false bass and a true bass voice and when to employ which.
First off, let's start with the definitions of the terms.
False Bass (or "Fauxbourdon") is a French term relating to the harmonization of plainchant melodies in which the bass would be a 6th below the melody; thus creating a serious of first-inversion chords as the organum would typically be harmonized a perfect-fourth below the melody.
I believe you probably meant to ask about vocal fry, which is like a falsetto, but for the lowest part of the vocal range.
A Bass range is approximately from E2 - E4 though some operatic roles necessitate further range extension. However, a True Bass range can extend much lower - typically down to Bb1 though many singers - especially Gospel singers and Russians can sing even lower still.
There is a joke in music: "Russia, where the men sing like men...and so do the women!"
As for expanding your range, like anything worth doing, it takes time. How much time and how much work are up to you - your results will show accordingly. Practicing too much can overtax your voice and lead to complications. Practicing too little will not yield desired results.
If you want to expand your range down, you must also expand your range up. Yes you can absolutely only work on low stuff, but you would only fully develop your low range when you developed your high range as well.
A simple exercise to do would be to start at middle C on the piano (C4) and sing downward chromatically to your lowest note. It should be relaxed; not forced. Try 3 times to sing the note clearly. If it doesn't happen, leave it be and try again the next day. The same should be done for singing upwards as well. The idea is that over time you will eventually develop the necessary flexibility to sing those pitches; thus expanding your range.
Another simple exercise for developing a purer tone and increasing flexibility would be to sing "Nae-Yah" (spelled phonetically) outlining a perfect-fifth interval with each syllable. "Yah" is held as you outline the descending triad and the final 5-note scale that outlines the original interval; which can either be slurred or articulated with "ha".
There are a plethora of vocal techniques to list that can help you, but most of them should be demonstrated in some way, and you would not otherwise glean any assistance from my answer. My recommendation would be to find a friend who is a trained vocalist and have them show you some warm-up techniques that will "open" up your voice and give you more flexibility.
Two more thoughts:
1.) Always warm up your voice by singing down before you sing higher (in your case make sure you sing higher as well!)
2.) Every voice is unique, and an adult man with a high voice is actually a very attractive sound. So much so that in Italy they use to castrate boys before they reached puberty so that their voices would not drop and they retained the boyish purity of tone with the presence of a man. Having heard a recording of one of the last male castrati I can say that it is quite a unique and mysterious sound.
At any rate, I hope those thoughts were helpful and answered your questions.
I've found this to be quite a challenge personally. Developing the bass tone is difficult precisely because focusing attention tends to induce muscular tension and raises muscle tone making lower vibrations more and more difficult to achieve.
If at all possible, do your practice first thing in the morning and stop when you notice tension rising.
Bass note require more breath support. Try to summon the note from below with a lot of breath. Tension is applied only to select the pitch; don't ever push lower by squeezing anything.