First, i wanted to say that the above advice are pretty good, keep them in mind as well...
Knowing that my first pieces were way, way worse than yours, i'll have to congratulate you, especially on the 2nd one you made (the red one)...
Now, given the chaotic and messy style i make my graphics, i'm not sure if any advice i can give can help you, but here goes :
I personally never knew the rule of threes, so i always tried the placement over trial and error. I copied (and hid) each render and background i used on every avatar and resized it and replaced it until i felt it looked good... On the aftermath of countless tries in the past i'd advise to keep the focal not centered to the middle of the avatar but 20-30% to the side (check Athdenald's CnC image and imagine i'd place the focal usually centered on either one of the vertical lines)... That helps me especially when i want to use background details and visual tricks as it gives more free space (if that makes sense at all XD). Also, i prefer the focal to cover more area than Athdenald's CnC, but that's entirely up to each artist and the focal to be used
Colors are covered almost perfectly, just keep in mind not to over-saturate your image in the end as in most cases it reduces the details of the work and may strain your eyes... again though, up to you

(a good trick is to add a gradient map layer (layer-> new adjustment layer -> gradient map) and play with both the colors and the blending options of it - that way, even if the background you really wanted to use doesn't fit the color sceme or the render looks a bit odd over it, you can adjust your result to your liking)
Text... So far, i've changed over a dozen text styles and i'm still not good at it... Athdenald's advice are the best i think, keep it simple and clear... You don't want people to first notice the text and then the work you made, so i'd add keep it a small font size as well.
On my chaotic makings, I also try to avoid to place the text over the focal at all if possible... I don't use colors on my text (most hate me for it XD) i just add a 1px 30% opacity black border (right click the layer, "layer properties") and i change the text layer's settings to "overlay" so that it takes after the colors of the overall picture directly below it... if not to visible i just duplicate the layer, rasterize it (again via right click) and use a soft eraser at various opacity to erase parts that stand out...
Last advice i have, also brought up above, is to make your focal look more natural with your background... many ways to make that possible, soft brushing the edges as Athdenald said is a really good and clean one...

Some more chaotic are to duplicate your focal if it's a render, then on the bottom layered render do a slight radial zoom blur (filter -> blur -> radial blur remember to select zoom instead of spin) at best quality (amount depends on the render size, i'd say a minimum of 30 maximum of 60?), then gaussian blur it (filter -> blur -> gaussian blur : no more than 3 pixels i guess?) and then erase of the top layer render the edges with a soft brush.... Then you can try playing with other ways, just gaussian, just radial, radial lightened (either ctrl+u or through the lighten filter), smudge, etc...
Overall, check other techniques used in tutorials, and try to mix the as you like them
I'm looking forward to see what you will be able to do in a month if those are your first tries