Melody as root note if I can't hear bass?
When I try to play by ear it's very hard for me to listen to the bass notes. Can I play the melody on bass string and build a chord from it? Would it achieve the same effect as if bass on root?
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Not really. The idea of listening to the bass notes is that generally speaking, the root is involved, often on beat one, and the bass line itself is fairly static.
Compare that to a melody line, where the root note may be used, but not necessarily, and many other 'passing' notes are apparent, that actually don't give much of a clue as to what the harmony in that bar actually is. True, there will be some notes from the underlying chord (not talking jazz here!) but not enough to latch onto, to give a good inkling as to what the chord/s might be.
The bass string on what instrument?
No.
Often the bass and melody are different tones of the chord, but only one tone is the root. So you can't necessarily use the melody tone as root.
But you can flip that around. The bass is not always the root. In pop/rock the bass usually is the root, but not always. That's a potential pitfall to expect all chords to be rooted on the bass.
What you really want to do is hear the chord as a complete unit. Depending on the musical style there is usually a key or mode for the music and you want to hear the chords as they relate to that tonality. Especially you should try to start identifying the sound of relative chord changes. For example, the sound of the movement of subdominant to tonic IV I is unique compared to moves to other chords like IV V or IV iv, etc. Chord changes can be heard and identified without literally figuring out the bass first.
I think the best way to build the skill is practice lots of standard progressions (there are a lot of standard four chord progressions) or two chord changes in all keys. Singing the chord tones while playing the chords will make the practice more productive. Combine that with working out songs by ear.
Playing the melody as the root note tends to make the music "thinner" in texture. In that case, the bass doesn't support the melody but rather just duplicates it. It's the same problem as parallel octaves in various types of music. The bass needs to be independent of the melody so these support each other. It's a simple experiment with a notation program to hear what happens (or on a piano or even a guitar.)
Can I play the melody on bass string and build a chord from it?
You certainly can and it will produce some kind of music.
Would it achieve the same effect as if bass on root?
No, not at all. Completely different. Here is a counter-example of a song that repeats a simple melody, which gets quite annoying on its own, but it's made slightly more interesting with chord changes.
When I try to play by ear it's very hard for me to listen to the bass
notes.
You cannot get better at hearing by merely listening, you have to play by ear. Find the bass note for one chord. Then another. And another. At every step it gets easier. The same with chords. Try something - did you get it right? Then try something else. Repeat. There is no shortcut, no magic trick, no Youtube video that makes you "get it". The only way is to practice.
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