Why is a supercritical fluid not a liquid?
Beyond the elementary school list of solid liquid and gas, there are many states of matter which exhibit peculiarly different properties. Wikipedia gives a list of the states of matter.
My book says that because in a container above the critical temperature and critical pressure, a fluid of density similar to liquid exists uniformly in the container and there is no surface or meniscus that separates the liquid from the gas.
That is true.
Does that mean that a liquid always has a meniscus which separates it from the liquid's vapour?
No, if the container is absolutely full of liquid then there is no gas phase.
Does that mean that in free space without no gravity, a gas/vapour will try to expand and the liquid will try to contract and form spherical blobs due to surface tension?
Yes, but for the liquid there will also be evaporation. The rate of evaporation depends on the temperature of the liquid. As evaporation occurs the liquid will also cool. If there is enough liquid in the blob, then the matter can get cold enough to form a solid which will then sublime.
Can I draw the conclusion from this that a liquid is the phase when attractive forces are dominant and repulsive forces are dominant in gas/vapour phase?
This is more or less true. I'd quibble about the nature of the "repulsive forces." I don't think that "repulsive forces" is the best way to model water in the form of steam. Rather the water molecules have too much kinetic energy to stick together.