In slang, it can mean "her dog is so big". I think that in order to use 'such' you need another noun after the adjective, so it probably doesn't fit.
no, while "ככה" and "כזה" have similar meanings, we use them differently. and "ככה" is not correct here. as mentioned earlier, using "כזה" in front of an adjective is like a slang way to accentuate that adjective.
no, in this instance, it's the equivalent of an american saying "her dog is so big!"
Yeah but Americans will put in the like (Not in a "CLUELESS" movie way but colloquially) if it's a comparison between something of a similar size. So you're saying that this is just commenting the dog is big vs the dog is (as big as)?