Blind vias connect an exposed surface with an inner layer, but do not go through the entire board.
Buried vias connect inner layers with each other, and to not extend into the top or bottom layer.
Microvias are drilled with a laser instead of a regular drill bit, usually in a process step before the layers are laminated together.
While there is no technical reason why blind and buries vias couldn't be drilled regularly, their main use case is in BGA breakout, where high density is important, and mechanical drills would be too fragile.
Thus, blind and buried vias are microvias.
A four layer board is constructed by laminating two thinner two layer boards together, and connecting these together. Blind vias can then be placed between layer 1 and 2, and between layer 3 and 4, and do not affect the other half of the board.
Buried vias become possible starting from four layers on -- 1-2, 1-2-3, 4-5-6 and 5-6 are possible options for blind vias, and 2-3 is a possible option for a buried via.
Using microvias and restricting the layers touched by the via mainly defines which drill file the coordinates go into, and which layers get a copper blob around these coordinates. It is perfectly possible to use a microvia through all layers as well.
Drill pair properties define which layers are manufactured together. Usually, 1-2, 3-4, 5-6 etc. go together, unless you have a strange stackup. In general, try to make microvias only between drill pairs, as manufacturing can become more expensive if there are additional drilling and plating steps even for the in-between substrate (here, normal vias should probably work fine.