How do you know when your independent findings are paper-worthy?
This is a very hard question in general, and is defined by a combination of absolute standards and community opinions. It's very hard to answer your specific question ("can I publish these results") and I don't think this community is the right forum to even ask that question. 

But your second question is a good one. There are some things to keep in mind:


make sure your ideas are indeed new. It's easy when working independently to be aware of the published literature, but not be aware of the large cloud of "folklore" knowledge that floats in the air of a community. You'll get a paper rejected because something is "well known", even though you can't find a specific reference and no one provides one. To figure this out, it would help to approach an expert in the field, or at least someone you trust. 
What kind of research you pursue is a complex combination of external trends and your interests. If you go too much towards external trends you might not find much pleasure in it. If you go too much towards personal interests (unless you have impeccable taste) you might find yourself isolated. It's all about balance. Similarly, while looking at current areas of research will tell you what's likely to be publishable, that's not the same thing as what's interesting or useful. Again, having some contact with people in the community might help a bit.