Liquid flux (ignoring the newer acid/water based type) is rosin dissolved in alcohol. Alcohol will not dissolve the petroleum base used in typical paste flux.
Gasoline or other petroleum solvents should work, but have too much evaporative fuming and are flammable. You're best off just using it as-is, apply it with a soldering pick if necessary and let the heat of the iron melt and spread it as was intended, or of course buy some liquid flux instead.
Paste solder can still be used for swipe soldering, you typically just need to make a swipe-pass one time to flow the flux then a second time with extra solder tinning the tip to solder the part down. It may be more trouble than it's worth to bother with this though, considering the cost of the projects and that a bottle of liquid flux is under $10 and lasts a long time if used sparingly.
Whether the flux already in flux-bearing solder is good enough depends on the joint, how oxidized the metal is, and what % of flux is in the solder being used. Personally I prefer to add flux when not in a hurry, because it tends to make the joint at least as good if not better and because often people put more solder than necessary on a joint only because they had to apply that much to get enough flux on the joint. Most people use maybe 2X as much solder as a joint actually needs and solder (especially lead bearing with lead prices rising over the past couple years) is more expensive than flux.