When a consonant and a vowel meet together, from where the sound start?

[m] is a nasal consonant, meaning, before the air escapes from the mouth creating the [ɑ] sound, it first escapes through the nose.

The articulation of [mɑ] has two steps, and therefore two places of articulation. The consonant is created by putting the lips together and opening the nasal passage-way, and along with vibrations in the vocal folds (this is a voiced consonant) creates the consonant [m]. The vowel requires open articulators, so the lips have to open. The vowel is shaped by lowering the root of the tongue to create the [ɑ] sound.

This can also be seen in a spectrogram (a visual representation of the spectrum of frequencies in a sound). You can see the differences in the sound waves (top half) and the concentration of the formants (bottom half) between the two segments, indicating two places of articulation.

This is the spectrogram of [ama], the two shorter red lines are the [a] vowel and the longer lower one is the [m].

As to [ɑ] changing into a variety of sounds, that could definitely happen. As vowels and consonants are rarely pronounced in "vacuum", and are usually very close to other segments, strange and magical things happen to them. For example the word "prince" can sound like the word "prints" if you don't pay attention and look at the the speaker. Or in the example above, pronouncing [mɑ] in rapid speech can cause the [ɑ] to become nasalized, which makes you sound like Fran Drescher.