
manch- (im Plural)
some
Means 'einige' (some) and refers to an indefinite number of people or things from a larger group.
Manche Leute mögen keinen Kaffee.
Some people don't like coffee.
some / many a
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some
Means 'einige' (some) and refers to an indefinite number of people or things from a larger group.
Manche Leute mögen keinen Kaffee.
Some people don't like coffee.

many a
Means 'so mancher' (many a) or 'nicht wenige' (quite a few) and is used to generalize an experience or quality that applies to several individual cases. It often has a slightly elevated or reflective connotation.
Mancher Traum wird erst spät im Leben wahr.
Many a dream comes true only late in life.
'Manch-' is declined like a definite article, for example 'dies-' (this). It agrees with the following noun in gender, number, and case.
Mancher Kollege hat sich darüber beschwert.
Some colleagues complained about it.
In the singular ('mancher', 'manche', 'manches'), the word often has a reflective or generalizing tone. It is used more often in written language and emphasizes that an experience applies to many individual cases.
Mancher Wunsch geht erst spät in Erfüllung.
Many a wish comes true only late.
Before an adjective, 'manch' can sometimes remain undeclined. This usage is rather literary or elevated.
Er erinnerte sich an manch guten Ratschlag seines Vaters.
He remembered many a good piece of advice from his father.
The expressions 'manch einer' (many a person) or 'so mancher' (quite a few / many a person) are fixed phrases. They refer to an indefinite, but not small, number of people.
Manch einer würde für diesen Job alles tun.
Many a person would do anything for this job.
much / a lot
Viel and manch can refer to numerous experiences or cases. Viel states the large amount directly, while manch highlights individual cases and has a generalizing, often slightly elevated or reflective effect. Use viel for a neutral statement of quantity, and manch for such individual cases.

Manch kritische Stimme hat dem Team geholfen, den Plan zu verbessern.
Many a critical voice helped the team improve the plan.
Viel Kritik hat dem Team geholfen, den Plan zu verbessern.
A great deal of criticism helped the team improve the plan.