Example: polar bear
I can only detect polar as an adjective and bear as a noun. But polar bear is actually a "noun". How do I obtain a free list of such?
Another example: hot dog.
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One thing that might help you is to know that often when an adjective and noun are combined to become a noun, there is a hyphen between the words, though the hyphen tends to get dropped as the compound comes into more general usage. The spellcheck on your computer may give you. I can't document this, but it seems to me that spellchecks tend to lag a bit behind general usage and keep the hyphen longer. Otherwise you just have to go with common sense and the context in which the words are used.
Though they may become so in the distant future, those are not (yet) compound words. The pair does not become a noun, grammatically. But you are right in noticing there's some extra cohesion between those words. If grizzly bears moved to the North Pole (at the risk of kindling that tinder-dry, global warming debate) it would be quite incorrect to call them polar bears. So if not grammar what kind of rule is this?
This is a phrasing or word use that means something different, or more specific, than the isolated words. Importantly, the meaning of an idiom is completely lost without precise wording. For someone learning English as a second language, these must be memorized over and above the meanings of the individual words. I would suggest you seek a list or book of English idioms.
This is an even subtler concept than idioms. Look for sites or books on the corpus linguistics concept of collocations. (In particular, see references there.) These compositional pairings are customary, relatively easy to infer from the meanings of the individual words, but if violated, jarring to a native speaker. I believe polar bear is more a collocation than an idiom.