MUltiple SIgnal Classification (MUSIC) Implementation
I'm going to group number 1 and 3 as related.

For a high level description of MUSIC, you can take a look at MATLAB's overview here. One of the main steps in the algorithm is to find the eigenvectors of a correlation matrix, which can be done via singular value decomposition or other methods. MATLAB has functions for this, so you may want to find equivalent functions in C/C++, or implement your own. The other steps in the algorithm are more implementation agnostic: mostly data collection and simple vector operations.

Using an N-element array, MUSIC can resolve at most N - 1 sources. These can be real sources or their images and must be dealt with accordingly.


For some more specific implementation details, I have an answer here where we go through the process of collecting data and performing MUSIC in MATLAB.