Please explain the meaning and description of ‘OM’.

Before all the physical creations came into existence, it is the sound that came first. The primordial sound is the sound of ‘Om’. In general, this ‘shabdha’ signifies welcoming God. It has three syllables – ‘A’ ‘U’ and ‘M’. When the first syllable ‘A’ is pronounced, one has to open his mouth fully. This represents creation. The second syllable ‘U’ represents sustenance or protection. The third syllable ‘M’ (pronouncing which the lips get closed) represents ‘laya’ or dissolution.
This is also called the ‘Pranava Mantra’. Yogis have this ‘dhwani’ (sound) resonating in their body. This is known as ‘anaahatam’.

Is organ donation after death acceptable according to our religion?

Organ donation is done as a social cause, with the welfare of someone in mind. So from this viewpoint, it is acceptable.

I was told that the Shastras do not recommend organ donation after death, as they do not really belong to us. Is organ donation right?

When we take the state of affairs today, we perform so many different deeds and activities against the Shastras towards our selfish ends and personal benefit. When it involves others, we try to find refuge in Shastras to discover a reason for not doing it.
When a deed is done for a social cause with the welfare of the people in mind, one can go ahead and do it.