Definitely the same as. I don't think we ever use the same with. Well except for Person A: Oh no! I forgot to lock my house today. Person B. Same with Jenny. Which means, Jenny forgot to lock her...
yes.
no. "like" is to say that two or more things are similar to one another whereas "same" means that they are more or less exact
exact, matching, identical, alike, duplicate, twin; indistinguishable, interchangeable, corresponding, equivalent, parallel, like, comparable, similar, congruent, concordant, consonant.