There is no difference between "this" and "that" nor "these" and "those" in German. "Dies"/"Diese"/"Dieser" and so on have no distance relation.
I give you an overview.
Dies ist mein Haus. (das Haus) ; Dies ist deine Küche. (die Küche); Dies ist sein Keller. (der Keller) There is no change in the word "dies" because the verb "sein(~bin, bist, ist,..)"(=the verb "to be") separates the "dies" from the other word, which is by the way in nominative, too, because the sentence can be turned around to: Mein Haus ist dies. These sentences works as well as with "das" instead of "dies" there is no difference.
Dieses Haus ist groß. Diese Küche ist sauber. (=The kitchen is clean. Well done Bro.) Dieser Keller ist dunkel. (The cellar is dark.) ~ Here the demonstrative pronoun is in contact with the word, therefore it gets declined.
Just like in English, in German the medial "s" occasionally sounds like a "z". As for the "r" at the end, it's not really there but that's how it sounds when pronounced correctly. In German, the "ie" cluster is usually pronounced with an "ee" sound, and the "ei" cluster sounds like "eye". My German teacher many years ago taught us to use the second vowel as a guide to help you remember!
It depends on the word that follows it. For instance, when it's singular it will be 'diese Kartoffel', while the plural would be 'diese Kartoffeln'. The actual 'diese' has no difference. The same thing often happens in English: for instance, there's no difference between 'the' when you're saying 'the potato' and 'the potatoes', its just dependent on the noun.