This is looking really nice now.
1. It's easy to miss that sort of thing when you've got everything else to think about.
2. I still think they're a bit near the body text but that's just me. If you're fine with it then keep it as it is.
3. That looks much nicer.
4. Sometimes you just have to go with what you've got.
5. The grey boxes make a nice difference.
6. If you've got a style to match then that's fine.
7. List looks much better now.
8. As with 5.
9. If that's what you want then that's your choice but adding the author shows more clearly that you're not quoting yourself. Not really important.
10. As with 5 and 8.
I have some more suggestions if you want them. I'm starting to get a bit picky now but attention to detail can be the making of a good document.
11. The grey boxes are a nice touch and help to separate the body text from the other stuff but the inside margin used is a bit "random". A major example is on page 3 where the bottom box has large margins but the top box has none at all. In other cases - e.g. page 5 - the margins are not uniform. Having the same spacing on all sides of all boxes would be a nice touch. It's not a major problem but it's one of the things that helps to put more of a "professional sheen" on a document.
12. The margins between the grey boxes and the body text are not consistent. For an example, see page 7. The gap between the bottom of the top grey box and the body text is smaller than the gap between the bottom of the body text and the top of the bottom grey box. Page 9, on the other hand, is more consistent in itself but not consistent with pages 1 & 2. This can be tricky to get right but it makes all the difference. This is where some planning from the start is needed.
13. There are two terms in typography that are important to learn: Widows and Orphans. Try this:
https://en.wikipedia.org/wiki/Widows_and_orphans for a start. Some examples in your document are: Widows - Page 1 Column 1, Page 9 Columns 1 & 3 (the heading and text needs to be kept together); Orphan - Page 7 Column 2. These aren't huge issues but changing things to lose the widows and orphans can put an extra bit of icing on the cake.
14. The font you have used for the headings has been outlined. This means that every glyph in a heading has been converted to curves. On large documents this can make a big difference to document size - if used for body text - as there is no embedded font file to read the glyphs from. To put it another way, instead of the font telling the system how to draw the letters, every single "A" (for instance, but it is the same for every single character) is represented in the document by a string of vector commands telling the PDF reader how to draw the letter. This also stops people from using copy and paste (which could also be a good thing). Also - see screenshot - display of some characters, such as lower-case L's, can look bad in some applications at certain zoom levels with outlines text. If you can't embed the font then you might have to change font or just put up with it but you should know that it can be an issue.
Points 12 and 13 should be addressed from the start of the document as changes will most often have knock-on effects later on. And if you're looking at things at this level then you need to look at using hyphenation too. Whatever you do, as you're making changes, remember to keep an eye on the end of your text chain to make sure you don't lose text from the end. There are whole books on this sort of thing so I can't really go into it more than this.
As for getting the body text to completely fill the space, go through all of the other points first and then see if you still have a gap. If you do have a gap, and you don't want one, then try having a look to see where you can add superfluous words.
For instance, the last paragraph could read (added words in capitals):
"With the BETTER understanding of the approach in the context of psychology and general behaviour it looks more promising that - IN THIS AUTHOR'S OPINION - at last, robotics can move out of the controlled conditions of the factory floor into the MORE unpredictable, AND dynamic real world to emulate the MORE intelligent, autonomous and EVEN psychologically advanced behaviour of humans and other COMPLEX living systems."
Just put extra words in and the gap will close up. Sometimes it's just that simple.