1) What is the exact meaning of the tinge?
verb (used with object), tinged, tinge·ing or ting·ing.
to impart a trace or slight degree of some color to; tint.
to impart a slight taste or smell to.
You should carefully consider various dictionary definitions before asking about the meaning of a word. :-) Or say why the dictionary definition is confusing.
2) What does mean the "all that's" and what is such a structure grammar?
"A tinge of garlic is all that's necessary" means
"All that's necessary is a tinge of garlic"
"All that's necessary is a small amount of garlic"
"Only a small amount of garlic is needed"
"A tinge of garlic is all that's necessary" is the same as
"A tinge of garlic is all that is necessary", which could be understood as
"A tinge of garlic is all (that is necessary)"
"all" is a predicate noun or predicate nominative. Like "Mr. Smith is a doctor" where "doctor" is a predicate noun.
The word "that" is a subordinating conjunction. "that is necessary" is an adjective clause modifying "all".
3) Must we use "in" or "for" in the specified position? The Grammarly takes an error and says it should be replaced with "for"!
Either "in" or "for" could possibly be used here. The word "in" might even be more preferable for this exact context than "for".