(1) You were taught wrong, because "I would like" = "Je voudrais," which is used in similar contexts in French.
(2) There is absolutely nothing here that suggests that you need the polite conditional form. "I want pasta without cheese" is not necessarily a request. You may not be asking anyone for pasta. "I want pasta without cheese for dinner tonight, so I don't need to stop by the cheese shop." (An awkward sentence, but the basic concept is that you can state that you want something without needing the conditional for politeness if you're just stating a fact, not making a request. "I want another cup of coffee. Can I get you one while I'm in the kitchen?"