Yes, reputable digital calipers are fine for thousandths of an inch. A micrometer is good for further precision and when you what more consistent measurements of softer materials. For example, if I measure my set of - gage pins, the caliper agrees exactly with the spec (a .210 pin reads 0.2095), and it's pretty hard to torque down too tightly on hardened steel. But if they were nylon and not steel, you'd probably get better repeatability with a micrometer. (And it's worth noting that the pins generally aren't actually half a thou smaller, a micrometer reads 0.20990. If 4 ten-thousandths of an inch are important to your project, yeah, you need a micrometer.)
Yup. These calipers that measure to .0005 of an inch only show hundredths of a mm (10 microns).
As for language, "thou", short for thousandths of an inch, is kind of the base unit in imperial machining. That's why the next one down is "tenth" in the vernacular. It's very confusing because 100 thou is one tenth of an inch, but you'd never call it a "tenth" even if "inch" is implicitly the base unit. Also confusing is that there are SI prefixes for all of these things, but they aren't in use. (Why not "milliinch"?)
Finally, one more advantage of the metric system; to measure 1 micrometer, you need a tool called a micrometer. That's easy to remember!
