Similar to English, as far as I know, you call your mother אמא when you are either addressing her, or are speaking to a sibling, who has the same אמא. So אמא = Mom, אמא שלי = my mother, typically.
It's implied. There is some ambiguity, but usually that's what it means.
I think, מַמּשׁ is not a degree word, but rather used for emphasis, giving special weight to to information that it is important: לְרִאשׁוֹנָה אֲנַ֫חְנוּ מַמָּשׁ יְכוֹלִים לַעֲשׂוֹת אֶת זֶה for the first time we can really do it or אֲנִי נוֹלַ֫דְתִּי מַמָּשׁ כָּאן בְּחֶ֫דֶר הַזֶּה מַמָּשׁ I really was born here in this very room. It is not so much about that it is true or very much the case, it is more about a forceful wow-effect.