can we read and program the microcodes of AMD processor?

Question 1

This article provides information on the microcode of AMD's Opteron (K8) family. It claims that it is not encrypted and provides information on the microcode format and updating the microcode.

Question 2

Anyone knows how to program microcodes? It's doesn't limit on AMD or Intel CPUs.

Not too many people do that kind of work. It's often written with a C compiler tweaked to generate the necessary microcode.

To answer your question in regard "is there other processors accepting microcode?" FPGA's are only programmed using such. These are not CPUs, what you program in them "is written at the hardware level". The microcode changes the doors and the result is your program. It can become very tedious as everything runs in parallel (true hardware parallelism).

Question 3

AMD microcode for recent processors is, indeed, encrypted and authenticated, much like Intel's. You need to have the proper crypto key to sign a microcode update the processor will accept.

Intel does it by embedding in the processor mask (hardware read-only) microcode a hash of the valid key(s?): the key itself is too large to bother embedding in the processor, so it will be present in the update data itself as seen here. Also, the Intel microcode update is actually an unified processor-package update data, it updates more than just the microcode for the decode unit. It can update all sort of internal processor parameters, as well as control sequences for other units than the decoder... it also has both opcode (and likely microcode) that the processor runs before(?)/after applying the update.