Not always. Both words can be used in positive sense to describe someone who is eager for knowledge, inquiring. Любопытный can also be used in negative sense to describe someone who is overly curious, prying. Eg. "любопытные соседи постоянно подслушивают, что у меня происходит". Любознательный always has a positive connotation. More often, though, любопытный is used to describe someone or something arousing interest, eg: он очень любопытный человек (= он очень интересный человек). Любознательный doesn't have this meaning.

No, you cannot. 1) "любопытный" has a positive and negative connotations. There are several expressions and sayings which use the negative connotation. For example, Любопытной Варваре на базаре нос оторвали. Любопытство кошку сгубило. Любопытному на днях нос прищемили в дверях. They are all frequently used. With the negative connotation, people say something like Не будь таким/такой любопытной. Не суй нос не в свои дела. (= Don't poking around. Mind your own business.) 2) "любознательный" has a positive connotation mainly. It is formed from two roots: "любовь" and "знать" and refers to a person who is eager to obtain knowledge — knowledge but not some information about one's neighbours or some gossips.

Carlos, to add to what was said above. There is a reason why I prefer 'любопытный' (and why some other people prefer 'любознательный') in positive sense. There is a bookish clichee: "I refer the curious reader to...." (means: a reader who wants to know more). Its Russian version only can have "любознательный" Meanwhile, in a biography of a scientist who thought "what will happen if you put a magnet near a wire?" (nothing interesting unless you are _moving_ the magnet) you would rather see "the curious researcher" translated as "любопытный". Despite this experiment changed the world, the scientist was driven by simple childish curiousity, and this is how scinece is done. "Любознательный" is more bookish word, often said for approval about a _student_. But this makes it is less 'human'. Любопытный can express an immediate _emotion_. Любопытный человек, is a person driven by this emotion. Любопытство is a feeling. "Чувствовать любопытство". Любознательность is never used to describe a feeling.

There is a good word - "Genesis" when the Earth was formless and void. Ask a question - What roots are those words derived from? Любопытный = любо (love) + пытный (=пытать - to torture/ to rack/ to put to the question) = the one who likes to spy out the invironment to get/ to pick up something new. Любознательный = любо (love) + знательный (=знать/знание = knowlrdge) = the one who lives the knowledge.

"Любопытной варваре нос оторвали". Это слово употребляется, когда кто-то хочет узнать про кого-то, или про его дела. Одним словом , вредный человек. Любознательный интересуется наукой, природой, читает книги, это очень умный человек.