Question

What is the significance of ॐ (Om/Aum)?

Answer

Meaning

Om denotes the supreme Brahma:

omiti brahma omitīdaṃsarvam [Tait. Up. - 1.8.1]
Om is Brahman. Om is everything here.

girām asmy ekam akṣaram [BG - 10.25]
Of sound vibrations I am the single syllable (OM)

But as we know God is threefold in nature, the same is the case for the single syllable Om. It consists of three different letters A, U, M which are the seed of all other letters, sounds, and words.

sa vā eṣa omityetadātmābhavat sa tredhātmānaṃ vyākuruta omiti tisro mātrā etābhiḥ [Mait. Up. 6.3] Meaning
He(God) came to have Om as his soul. He divided into three parts. So Om is the three units (a,u,m).

Significance

Now the letters A, U, M can be signified differently as Brahma, Vishnu, Siva, or creation, preservation, annihilation, or satva(goodness), rajas(passion), tamas(ignorance). The Mandukya Upanishad which deals only the pranava (Om) defines the three units as below:

jāgaritasthāno vaiśvānaro'kāraḥ prathamā mātrā [Mandu. Up. - 9]
Waking state is the first unit (A)

svapnasthānastaijasa ukāro dvitīyā mātrā [Mandu. Up. - 10]
Dream state is the second unit (U)

suṣuptasthānaḥ prājño makārastṛtīyā mātrā [Mandu. Up. - 11]
Sleeping state is the third unit (M)

These three states are related to a person. But these are also synonymous to creation, preservation, annihilation and other meanings when analyzed from the universal point of view.

Usage of Om at the beginning of mantras

Om is the primeval sound from which everything originated. By Om speech is held together:

yathā śaṅkunā sarvāṇi parṇāni saṃtṛṇṇānyevamoṃkāreṇa sarvā vāksaṃtṛṇṇoṃkāra [Chg. Up. 2.23.3]
Meaning
Like with a spike(stem or branch of a tree) all leaves are hold together, through the syllable Om all speech or voice is hold together.

So it is said that, without the presence of Om at the beginning all the following letters of the mantra will fall apart and hence won't work. Om at the beginning holds the rest of the mantra together. So on a similar context the Manu Smriti also says:

Let the Brahmin always pronounce the syllable Om at the beginning and at the end of (a lesson in) the Veda; (for) unless the syllable Om precedes, (the lesson) will slip away (from him) and unless it follows, it will get scattered. [Manu - 2.74]

Om is the seed mantra from which every other letter and mantra originated. Hence, om goes at the beginning of the Veda mantras while reciting it. Because chanting of the Vedas begins from Om, it is also known as udgitha (chanting of Veda mantra).

omityetadakṣaramudgīthamupāsīta [Chg. Up. - 1.1.1]
One should worship Om as the udgitha

I think this answers all the four questions you asked.

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