Learn English – Can “quite” modify adjectives and adverbs in the comparative degree

The construction preposition + "there" is informal and probably fairly recent. Or perhaps it is better to speak of three different constructions, because the meaning of each one is not based on the meaning of the preposition in the same way.

There's a huge market out there.

It is best to think of out there as a fixed phrase. It means something like "in a place outside". If you would have to analyse it, perhaps you could say it is like a double adverb. The word out is used adverbially to mean "outside", which is generally possible; the word there is an adverb meaning "away from me, the speaker". So then the compound meaning would be "outside and some distance away from me/us". That is more or less what the phrase means, I would say. Derived from this is the figurative meaning "eccentric, strange" for a person: she is really out there.

The book is over there.

The phrase over there is also informal and probably best treated as a set phrase. It means more or less the same as there. The word over is more generally used in informal language with locations: let's go over to my place, she is over at my place. It adds very little meaning to those sentences—perhaps an added sense of "removed from the speaker", derived from phrases like over the river, over the ocean. Similarly, it adds little meaning to there is over there. You could say it is used like some sort of particle or adverb to emphasise there, but it is really impossible to analyse. The same applies to over here.

There are people in there.

The phrase in there is, again, probably best considered a set phrase meaning "inside that place", for instance inside a house or inside a box. It is slightly informal. You could say in is used adverbially, similar to is father in?, which means "is father in the house?". Or you could say it is a preposition that treats there like a noun meaning "that place": "inside that place". While there is not normally a noun and normally does not take a preposition, it still seems to be like that in this case. Relative pronouns of location can sometimes also do something with prepositions, as in the place from whence she came or from where she came, or wherein (legal language).

From there you need to take the train to Oxford.

The phrase from there can be analysed the same way as in there, as preposition + noun, where there means "that place". In from here, the word here would then mean "this place". The phrase does not sound informal at all to me, which may indicate that it is an older phrase than the ones above.

Go from here to there.

The phrase to there clearly seems to be constructed as preposition + noun. In this context, at least, it does not sound especially informal; but in most cases you would just say there (not to there) when it immediately follows a verb: she went there is normal, not she went to there.

As you see, not all of these phrases seem to be of the same kind. The last three are more like preposition + noun, the first two are perhaps different.