As for melody while singing? I can do it and if I can, so can you. Here's a tip on how to start. Play the major scale from one of the lessons here. Play the eight notes of the scale. Example: C D E F G A B C. Play this scale until you can play it smoothly without any effort at a comfortable tempo. Many of you reading this post are well beyond that. If so let's go to the next step. Sing that scale as you play it. You can sing the names of the notes, you can call them by numbers, it doesn't matter. When you can sing the notes along with playing them on the guitar you are ...playing melody and singing at the same time.

When you can do this, play the melody simple songs. "Mary Had a Little Lamb", "Twinkle Twinkle Little Star" in C and sing them. Now you are doing two important things One-you've picked a simple melody by ear because you've learned the tones by playing and singing your scale Two- you're playing melody and singing at the same time. At this point you can branch out. I love old time music. If you do as well, you're in luck. Take the fine Wildwood Flower lesson on this website and learn it. Listen to the Carter Family recording and learn the words. Listen some more and see how Mother Maybell works the simple melody. Most of her instrumental breaks stray very little from the melody and parts of them are easily inserted while singing and strumming. 

These elements are not impossible yet seem mysterious and unobtainable at first. Chip away at them a little bit every time you play. Every granite statue started with that first chisel stroke.

https://www.youtube.com/watch?v=OrbdS7d8B20

Hubby & I set aside late Saturday afternoon and sometimes into the evening for singing/strumming sessions. I'm trying to teach him and he doesn't have a lot of time to practice during the week, but we still have a lot of fun. He really struggles with singing while playing but he just keeps trying, bless his heart. I know one day it will click for him. 😀