How do I know if my board is classified as micro electronics?

The below specifications can be termed as micro electronics:

30 micron lines / spaces (1.25 Mils)

Very thin film build up down to 1-mil thick

Laser hole drilled as small as 2 mils  

Where do I find these applications?

Mainly in flip chip packages, chip scale packages (CSP), and build-up substrates. The end applications are: smartphones, digital still cameras, and next generation compact packages.  

Can microelectronics have blind and buried structures?

Yes, you can have blind and buried vias in your micro PCB.

What will the surface finish of these micro electronics be?

The surface finish for micro boards is soft gold. Usually, we have a wire bonding process.