Burden of proof and Occam’z razor

Yes this is directly related to my very previous question and I can’t help but ask this one too so please bear with me.

Very  specifically , who has the burden of proof? If someone claims something ordinary like owning a cat, and then a person claims he’s lying, then who has the burden of proof in this case? From what I understand, the owner has to prove they own a cat, right? If this is so and everything required solid evidence, then really it’s not practical nor realistic nor even reasonable, correct? If the burden of proof is on the one who’s claiming they’re lying, then is it because of probability and Occam’z razor? The probability of them actually having a cat in a normal situation is fairly high, and so does it follow that the default position is that they’re saying the truth? Is this what Occam’s razor is all about then? (That the default position is with the highest probability?)

Finally, sorry for the many questions :P

The person making the claim has the burden of proof. If someone claims they have a cat, it is not practical nor reasonable to demand evidence for that claim, and if someone were to demand evidence, the person would simply say they don't care if they’re believed or not.

The Burden of Proof is only a thing in argumentation. When one's goal is convince another that a claim is true, they have the burden of proof. If the theist claims God exists, they have the burden of proof. If an atheist claims that God does not exist, they have the burden of proof.

First, Occam’s Razor doesn’t apply.  That’s the principle that all other things bring equal, the simplest explanation should be preferred.  So if a phenomenon needs to be explained, a simpler explanation should be considered rather than a more complicated one.  As additional information is obtained, the theory may need to be revised and become more complicated to accommodate the new evidence.  But that has nothing to do. in your example, of who owns the cat. 
Burden of Proof is a legal concept.  The party making the claim has the burden of proof.  So if I claim the cat you’re keeping us mine, I’d have the burden of proving it.