Well, "dieser" can be a determiner (so it indicates case and gender of a noun phrase), or a pronoun.
In each instance, it sort-of declines similarly to the definite article "the". So:
Nom: Masc/Fem/Neut/Pl = dieser/diese/dieses/diese
Acc: Masc/Fem/Neut/Pl = diesen/diese/dieses/diese
Dat: Masc/Fem/Neut/Pl = diesem/dieser/diesem/diesen
Gen: Masc/Fem/Neut/Pl = dieses/dieser/dieses/dieser
So your "dieser" and "diesen" are up there, too.
When used as a pronoun, "dieses" is often replaced by "dies". Also, "dies" can be used whatever the gender or number, in the sense of "this/these", so:
Dies sind meine Äpfel (these are my apples) Dies ist meine Uhr (this is my watch).
As a determiner, "dies" sometimes replaces "dieses" in writing, in the Neuter Nom/Acc, too.
Genug von dieser Grammatik!
Indirect objects are when an action is done to or for someone-- her in "I brought her lunch" or "dog" in "I gave the dog water". (sorry, I haven't covered the Dative case yet so I'd almost certainly decline them wrong if I tried to give an example in German)
Here, Buch is accusative case and a direct object, the action being performed on it. Like "football" in "I kicked the football" or apple in "I bit the apple"
Yes, they're all three correct.
German doesn't distinguish "this/that" as strongly as English does, and never made the split between "that" and "the" that English made several centuries ago, so those are still the same word -- the definite article and the basic demonstrative pronoun/demonstrative determiner are identical in German.