But wouldn't dem Hund be just [to] the dog?
No. der, die, das (in any of their forms) mean both "the" or "that", and are often also used for "this".
English split up that word into two separate words "the" (originally from the masculine form) and "that" (originally from the neuter form), but in German, the same word still has both meanings.
LEO is indeed very useful, but I wouldn't use it as a bible -- there's a lot of good stuff in it (and even more good tidbits to be found in the forum discussions there), but some of it I wouldn't necessarily trust.
Of course, without being fluent in both languages, it's nearly impossible to know which bits are less useful....
Do you know of a better online German dictionary/ language handbook though?
No; I don't know of any dictionary that's 100% reliable.
Sometimes Linguee can be helpful as well, but I've found that overall, the quality is lower, since it gives you lots of quotes from websites, not all of which are written by educated native speakers, so the quality of the language there is not always what you would expect from a professionally-created dictionary.
Yes, "diesem" is the Dative form for masculine singular nouns, but it is also the Dative form for neuter singular nouns.
Geben trigger accusative, right?
geben generally takes two objects:
- a direct object (the thing which changes hands), in the accusative case
- an indirect object (the recipient), in the dative case
You give something (DO) to someone (IO).
Why is this dative?
Please be more precise -- what do you mean with "this"?