The red signposts at 68 and 76 indicate a non-standard barline. In some cases that means a hidden time signature; in other cases it means a barline that isn’t defined by the time signature. In your case it’s a barline that’s not defined by the prevailing time signature, even though it’s in the same place a standard barline would be. If you select and delete the barline immediately before the signpost (at the end of bar 67 and at the end of bar 76) you’ll find that the signpost disappears.
I can’t see anything odd at bar 78 - there’s no signpost there as far as I can tell. Maybe you meant 73. If so, same as above. My guess is that in all these cases you added a barline manually, then later decided to define the time signature as 9/16 (or 2/8 or whatever). It’s the adding a barline manually that causes the red signpost.
As to increasing the short note note spacing, I couldn’t replicate the issue of System Breaks being inserted mid-bar; I did find that Dorico would be forced into putting e.g. a single 1/8 bar on a system of its own (as it was immediately followed by a purple System Break signpost that had been manually added).
edit: I could indeed find an example of Dorico doing this, but I’m not sure you can have it both ways: if you’re defining a minimum space for short notes, and telling Dorico not to split bars across systems, and filling a bar with notes such that the width of those notes plus four spaces between each of them results in a longer system than the width of the page, Dorico has to break one of those rules.
I think actually increasing the Note Spacing value for short notes to 4 spaces (the default is I think 1 3/5 spaces) is going to make your accidental collision situation worse, not better, as you’d be asking Dorico to put an unnecessarily large gap between each short note, even single notes that have no accidentals at all. This prevents Dorico from using the extra space in a system where it’s actually needed. Try getting the layout the way you want it, then Lock Layout (from the left panel of Engrave mode), then decrease the Note Spacing value for short notes, and I think you’ll get a much better automated result.
The fact of the matter is that Dorico does aim to be reasonably even in its spacing, and that does mean that if you have stacks of accidentals they won’t necessarily all be handled well, and some manual Note Spacing adjustments may need to be made locally (using the Note Spacing submode of Engrave mode).