Dissolving sugar in water changes sugar(solid) into sugarwater(liquid)

2) They both weigh the same. But the 1kg of lead the matter is more compact thus in a smaller size. 1kg of feathers the matter is not as compact and thus in a bigger container. I rather carry 1 kg of lead.

3)density is the mass per volume, in other words the amount of matter in a volume. The more matter in a volume the larger the density and the heavier it is. Thus it will sink.

4)density can be useful in determining whether a substance is pure, as in pure gold has more density than gold mix with silver (because silver is less dense than gold). Also different substances have different densities. Example water at 20degrees celsius has .998g while lead has 11.3g at the same temperature, thus you can determine the substance you are using by determining the density and in turn determining the substance at hand.

1 kg of lead. Either way you’re carrying a kg. The lead is just less awkward to carry.

it will sink

Density helps to measure irregular objects (rocks etc.) that can’t be measured using the length x width x height formula. (I’m not entirely sure this answers your question, but I tried)