Very little, either can be used to mean "This" or "That". However in this case, because Suppe is a feminine word, you would use "Diese Suppe" to imply "This soup". You could also say "Die ist eine Suppe" which means "This is a soup". You wouldn't use Das (Although you could say "Das ist ein Kind" to mean "This is a child").
While it can mean the same thing as "Die Suppe schmeckt süß", they are not exactly the same sentence and can imply different details.
The sentence "This soup tastes sweet" implies the person has actually tasted the soup and is giving an observation about it.
The sentence "This soup is sweet" implies that it is a characteristic of the soup or the type of soup, ie that it is intended to be sweet.
It would have to be die since soup is feminine, but I think if the definite pronoun is going directly before the noun, die means the, and if there is a verb or preposition between the definite pronoun and the noun, you can use das. So you could say "das ist ein Hund". That is a dog/This is a dog. But Der Hund only means "the dog"
Not so easy! Remember German is inflected, so words like dieser must account for gender/number and the 4 cases. It looks like Duo gets there, so suspend that thought for now, or you could look up the 4x4 grid for dieser-word declension. I think they decline just like the definite articles der, den etc....
Because in Dies sind Katzen, dies stands alone to introduce something new to the conversation -- we do that with a neuter singular word in German (das or dies) regardless of the gender of the thing(s) you are introducing or how many there are.
But in this sentence, diese stands before Suppe -- it's clear to which noun dies applies and so it has to match Suppe in gender, number, and case, so it stands in the feminine nominative singular form diese.
There are a number of words in German that act differently when they are before a noun and when they are not, and this is one such word.