Oh boy, no it does not. Supporting low-intervention markets (i.e. brutal competition among corporations) alongside high taxation of gains (and strong services for individuals) is absolutely coherent and both capitalist and not right wing. (It's a decent description of my politics.)
Wouldn't say that. I like wealth redistribution and taxation as a tool of both economic empowerment and political equalisation.
I do have friends whom I'd consider left wing. I agree with them on many issues, from unionising bars to raising the minimum wage. I disagree with them on others, e.g. regulating everything for the sake of it.