Liberal means advocate of human rights
Not unless you're creating your own personal definition. At best, liberalism means advocating for individual rights, and where you or I might disagree with the application of that idea is where individual rights are in tension with communal or collective rights more broadly
In what way does exchanging money for goods cause outlawing gay marriage or banning books?
Markets are not the same as capitalism. It's a description of a system that enshrines abstract ownership over systems of production. If you dont take issue with the coercive mechanisms within capital relations, then im not really sure where to put you 'on the left'.