Dan and the pKa table he gave are correct. Amides are not particularly basic, specifically because of the withdrawing carbonyl group. Amides are protonated at oxygen and their basicity is closer to that of water and alcohols than it is to amines.
If anything, the additional methyl group on methylhydrazine will make it more basic than hydrazine itself because alkyl groups are electron donating relative to hydrogen so they help to delocalize the positive charge in the protonated form.
As a general rule: electron donating groups=more basic and less acidic, and electron withdrawing groups = more acidic and less basic.
I'm not sure what you mean about negative charges on hydrazine; there are no resonance structures with formal negative charges on any form of hydrazine or methylhydrazine. And also there is no resonance delocalization in hydrazine, at least not in a way where you can draw a reasonable resonance structure as you would in sophomore organic.