Others have hit on question 1 sufficiently that I'm not going to rehash it here, but I did want to hit on question 2 a little, because it seems (to me) the more interesting one.
So, when someone is asking you this type of question, they are less concerned with what your code looks like, and more concerned with how you are thinking. In the real world, you won't ever actually have to write multiplication without the * operator; every programming language known to man (with the exception of Brainfuck, I guess) has multiplication implemented, almost always with the * operator. The point is, sometimes you are working with code, and for whatever reason (maybe due to library bloat, due to configuration errors, due to package incompatibility, etc), you won't be able to use a library you are used to. The idea is to see how you function in those situations.
The question isn't whether or not you are "cut out" to be a programmer; skills like these can be learned. A trick I use personally is to think about what, exactly, is the expected result for the question they're asking? In this particular example, as I (and I presume you as well) learned in grade 4 in elementary school, multiplication is repeated addition. Therefore, I would implement it (and have in the past; I've had this same question in a few interviews) with a for loop doing repeated addition.
The thing is, if you don't realize that multiplication is repeated addition (or whatever other question you're being asked to answer), then you'll just be screwed. Which is why I'm not a huge fan of these types of questions, because a lot of them boil down to trivia that you either know or don't know, rather than testing your true skills as a programmer (the skills mentioned above regarding libraries etc can be tested much better in other ways).
