I know this sounds crazy. I did find videos guiding you to fingerpick given you know how to to hum.
Should I first remember how each string sounds at each fret?
YES! If you know how to hum a tune then you can obviously recognise it enough to regurgitate it ! So ...
You can 'find' it on a guitar. It'll be on there somewhere so learning to play it follows if you just search about with your fingers ont he fretboard.
Humming plays just one note at a time so it's ok for learning a tune / melody but not for working out chords. For that, you can either find a song book (internet is your friend here) which will give you chords for the song, and there are a zillion websites telling you how to play those chords.
The alternative is to work this out for yourself. You may get a deeper undertsanding of music & chords that way (a bit like the difference between reading about how to tap dance and learning it for yourself from scratch). However it's easy to get into some bad habits if you learn for yourself too much.
Generally speaking there are lots of resources on the internet to help you with this: youtube, lyric & chord sites, etc. Google will help you out.
It's not easy 'remembering how each string sounds at each fret'. In fact, that's not a lot to do with learning to play guitar - or any instrument. You may find that RECOGNISING the sound of open strings will be helpful as well as being able to tell if one note is higher/lower, a bit/lot higher than another. As the first answer says, if you can hum, you can probably play an instrument. It's working out how to make sounds, where to put fingers and how it all fits together that makes it challenging - and fun. Videos are o.k., but ask them a question, and there's no response! A teacher will always be your best move, in the initial stages, at least.
Yes, humming is melodic -- one note at a time (for most people). You may easily develop a "linear" style of sliding up and down a single string for your melody. Depending upon the range of notes, you may have to switch strings. Overall, a sliding "linear" approach is very straightforward.
In time, the other strings are there to support harmonic playing -- more than one note at a time. The guitar, like the piano, offers rich harmonic possibilities.
Keeping it simple, with a melodic approach to using individual strings, will allow you to play like you hum. So, yes, bring your musical ear & mind to the guitar and enjoy yourself!