You cannot have two visas at the same time. One will be cancelled i favor of the other. If you currently have B1 then applied for H1, your B1 will be cancelled. If you already have H1, there's no need to apply for B1 since it serves same purpose. THe only difference is H1 has a longer validity...
It is not possible to do it yourself. You can only obtain permanent residency (greencard) through an immediate US Citizen relative (parents, brother/sister, children) or through employment.
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