Good for you sticking your neck out and taking the first steps toward financial freedom. They aren't dumb questions at all.
There's nothing wrong with buying properties for cash, but that doesn't necessarily reduce your risk. I would argue that investing in multiple properties with a downpayment diversifies your investment and reduces the chance any one property will go south. You also reduce your cashflow risk, vacancy risk, and market risk.
Additionally, many people will loosely equate risk with cap rate. There is usually a reason the cap rate is higher. Investing in a less desirable community with cheaper houses will usually result in a higher cap rate but the vacancy or market risk is likely higher. In an A+ neighborhood with high demand, the cap rate will be lower but the vacancies are also lower and the demand is higher. Everything is a trade-off. With the example you gave, investing out of state has its own risks that may or may not be worth the difference in cap rate. Real estate is much more than a numbers game.
As far as using leverage eating into your profits, I think if you look at the numbers, you will find that the opposite is true. You should research the difference between cash-on-cash return and cap rates. If you are paying cash, your cap rate and cash-on-cash return are the same. When you leverage, your cash-on-cash return will increase exponentially, returning far greater returns on the same cash out of pocket.
Don't take my word for it. Use the BP calculator and run the numbers on buying a couple houses for cash vs. using the same cash to buy houses with 20% down. Factor your financing costs, etc and see which strategy comes out ahead.
Finally, if I could invest anywhere, I would still invest in a market I know. That being said, I live in Colorado Springs and I typically invest in a one-hour radius. I can still visit the properties if I want to or need to, but I can take advantage of opportunities in cheaper markets.
Hopefully this is helpful. Best of luck to you in your investing journey.