I have a list of companies with sales in the $5-10M range and I would like to determine whether each company possesses the characteristics shown below. What source or database can I use (preferably free) to determine this?
Recurring, high margin, growing
Diverse (customers, products & markets)
EBITDA margin of >15%
Growing or stable industry that is not cyclical in nature (how “recession-proof” is this industry)
Fragmented competitive landscape
Low threat of external shocks – technological, regulatory, legal, environmental, fashion, etc.
Simple, understandable operations
High return on invested capital
Identifiable areas of improvement
Underfollowed or misunderstood in the industry

Half of those attributes won't be in anyone's database. They are too vague and subjective and changeable over time.
Second, you are asking for two very nearly impossible attributes: good solid bet for growth and stability, yet underfollowed, etc. There are hundreds of investors who have already identified such gems, and they aren't going to disclose them unless they want to hype the stock to increase it's price.
They do it with diligence and lots of work.
You can find out a lot about companies by joining a large fund like Vanguard (as I suggested before).
They have some of this list in their database.

Going by this list isn't going to guarantee a return on your investment.
It's like buying SCUBA gear and jumping into the middle of the ocean in a typhoon.

Immerse yourself in TV - CNBC and Bloomberg. Follow all the investment blogs. Motley Fool, etc. Read about new companies as they appear on fund pages (again, Vanguard, Fidelity, Schwab, etc). Look at Morningstar. Call Jim Kramer's live show at 6 pm, LOL.

You MUST make this a full time job at first. Actually I don't know anyone who succeeds any other way, forever. Unless you take investing as a long term deal, picking a diverse group of stocks that you feel good about and have researched thoroughly, and you can afford to weather all the storms, BUY INTO A FUND and let others do the work.