La première entrée

When letter 'a' is followed by 'im' or 'in' at the end of a word, and there is nothing or only consonant after, you pronounce the combination like the French word "un", as in:

demain
j'ai faim
Américain
une crainte (a fear)
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When letter 'a' is followed by 'il', 'ill', or 'ille', it's pronounced separately - 'a' as in 'father', then the English letter 'e', like these words:

de l'ail (some garlic)
un détail (a detail)
un travail
une bataille (a battle)
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'an', is pronounced as the French word 'en' when by itself or followed by a consonant:

un an
grand

but if followed by a vowel OR another 'n', then it is pronounced separately as 'a' and 'n':

un animal
un anniversaire  (a birthday)
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'am' is usually pronounced separately, but when followed with 'p' or 'b', it is pronounced like 'en':

un champ (a field)
un vampire
une ampoule (a lightbulb)
une ambulance
un champignon (a mushroom)
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'au' is pronounced as the French letter 'o', or the 'au' in English 'August':

aujourd'hui
aussi
chaud
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'ay', is pronounced like é, then followed by the natural sound of 'y', like the letter 'e' in English.

payer
essayer  (to try)
un pays  (a country)