Not truly. If you have hate in you, you can't show love. Let the hate out and the love will fill you, if you want it.
Of course you can. You might be an insecure burden upon your loved one but it is certainly possible to love someone. There is no simple answer to this question really. While I say possible, I doesn't necessarily mean likely, and self hatred comes in so many forms.
Love someone if you hate yourself? Yes, but only if you dress up in a prison uniform and have them spank you with a belt regularly.
When I get to those moments where I hate myself, I am not prejudiced...I hate everyone equally as much.