Technique, lens, film flatness, and the focusing calibration of your camera will affect your sharpness the most. No developer will correct for shaky technique or a lens that isn't sharp. So, no; it won't improve the sharpness of pix from your toy camera in that way. However, if you dilute it a lot, it will accentuate the sharpness of anything that really is sharp on the negative. What I am saying is that it cannot make a soft lens sharp, or cover up for any other technical issue, but it can increase the sharpness of whatever is already sharp.
I usually use it at 1:50 or 1:100, though I have used it at 1:200 just to see what would happen. I don't see much reason to go to 1:200, personally.
You usually start to see the haloed edges and extreme grain once you go to 1:100 and use a minimal agitation or standing development routine. I use it at 1:50 for normal negs, and 1:100 for "special effects." I've never tried it at 1:100 for normal development, so I don't know what it looks like.
HC-110 is a very good general purpose developer that is available off the shelf. It will be kind of like using Rodinal in that they are both highly concentrated from the bottle, and you use very little concentrate to make up your working solutions. However I think HC-110 is a "better" general-purpose all-around developer due to how versatile and forgiving it is. IME and IMO some films just look "weird" in Rodinal, no matter what dilution. There aren't any films that give me trouble when using HC-110 (or D-76, or X-Tol, etc.) It doesn't get a whole lot easier to use than HC-110, unless it is Rodinal or pre-mixed PMK pyro. No powders, no clip tests, etc. It keeps forever and develops film exactly the same every time IME, no matter how old. My problem with powdered mixes when I used them was inconsistency from batch to batch. I had to make it up fresh all the time in small batches to get the consistency I wanted...and I hate mixing powders. YMMV.