Some rare passing trans identified males may. The rest don't experience misogyny.
The majority of the misogyny I've experienced is sexual harassment. Trans women tend to experience this as soon as they vaguely pass. There's so many posts about it; having to come to terms with being catcalled, or strangers thinking they have the right to touch you. I think some people have a sexual fetish for feminisation which can often be applied to trans people.
They are just as likely to be viewed as weak/stupid because of misogyny. Trans men are made fun of by misogynists for trying to ascend to the male level. Trans women are mocked because now, they see them on the same level as women.
I think trans women often get the hit of the gender pay gap once they've transitioned, too.
No, cis means that you identify as a woman. Cis is unnecessary, it's a label that isn't needed, isn't wanted and doesn't describe me.
It's not necessary in general conversation. In some discussions it's very helpful as a way to differentiate!
I'll ask again - how do you feel about your erasure?
I don't really feel erased 
Trans women are women, okay, so am I. I'm still here.
Just because discussions about trans people aren't centred on me (obviously) doesn't make me "erased"!