Can heat be transferred by thermal conduction in liquids?

of course. In a way, even all convection ends with conduction anyway (when you get right down at the molecule to molecule interaction, that is conduction when energy transfers from one to another). That is, although convection moves heat by mass, the individual particles do not give energy to adjacent particles by convection, and that transfer has to occur to achieve equilibration, so it either occurs by collision (conduction) or by radiation..

Yes. Conduction can occur in solids, liquids and gases.

(There will also be convection and a tiny amount of radiation inside the liquid.)