You got this white dog from me, right? - Tőlem kaptad ezt a fehér kutyát, ugye?
There are definitely times I have asked someone if the thing they have is the one i gave them as a gift so I am wondering if this sentence works that way. Probably i would know in the case of a dog, but if someone is wearing a scarf and I'm wondering if I gave them that scarf (because I vaguely remember the gift and not sure if that is the same scarf) I can see a question like this one.
is there a difference in meaning between entolem vs tolem (and any other combination pairs)?
Not really. As always, the addition of the pronoun gives some emphasis to the word: éntőlem - it is from me, not from anyone else.
In what kind of context would this be used? Could I say it to express that the dog is mine? Or is it more like 'this is a present from me to somebody'?
No to the first one, you can't use tőlem to express "the dog is mine."
But yes, tőlem van means it's "from me" - a gift I gave, a letter I sent, something like that.
A gift from Jacob to Jan would be Jacobtól Jannak and a gift "from me to you" would be tőlem neked.
That still leaves us with the fact that this is a slightly weird sentence (presumably the speaker should know whether the dog is from him or not).
Yes, it may be slightly weird with a dog. But basically it is saying that the speaker does not remember or is not sure if she or he gave this dog or whatever, as a present, to the other person. Happens to me a lot.
If the question comes from a dement Person, it could be a possible question.