Technically speaking, no. The mantle, which is solid, comprises about 2/3 of the Earth's mass. However at a planetary scale solids are not rigid enough to maintain their shape, so the Earth is closer to a liquid held together by gravity than to a rigid solid object. See this simulation for an interesting demonstration of its properties: https://youtu.be/kRlhlCWplqk
I don't believe the "solid" core is solid in any sense of the word we can relate to; kinda like how Jupiters volume is mostly gas, yet 99% of that is at densities greater than the Mariana trench — where you would vaporize, and would feel more solid to us that anything we've experienced — and the "solid" core is more like a molten hydrogen liquid; hotter than the surface of the sun (but not hot enough for fusion).
The correct answer is we don't know. There are novel (to us, anyway) states of iron, for example, that exist at extreme temperatures and pressures that have led scientists to postulate on the possible existence of a crystalized iron core, within the already solid inner core.
The mantle is a large part of the Earth's volume and even though it flows over geologic time scales, it is still considered solid. Then there's the crust and inner core, which are also considered solid. IMO the Earth is closer to a balloon filled with flour and a small iron ball in the center.
Liquid doesn't mean just water. I think what op was getting at that the molten core of the earth is in liquid(-ish?) form, thus the water balloon idea.
Depends upon how you're seeing liquid. If you just mean water, definitely not. If you mean things that behave like liquids behave or are in their liquid phase (is magma liquid here?) then I'm not sure