

Liberal Democratic Party is the name of the party, they are conservative in Japanese politics.
‘liberal’ in general political discourse doesn’t mean ‘left-wing trending towards communist’ as it is used in American communication, it is simply the historical opposing view to absolutism (e.g. Absolute monarchy). Liberal thought centers around individual freedoms; modern-day conservatives advocate for permissive individual freedoms by limiting government’s role in as many facets of life as possible (in theory, real parties and platforms have little to do with their marketing). Modern-day liberals advocate for positively identfying and enforcing freedoms through law. Illiberal thought is common in the west, and advocates for limiting individual freedoms for one reason or another - Germany’s prohibitions against Nazi speech, and the US’s restrictions on recreational drugs are examples of illiberal policies.
UN votes are largely symbolic, they have no actual policy function in almost all cases - member states must create and ratify separate treaties for that.
Removing the veto just leads to the veto-holders even more flagrantly undermining the UN’s authority.