Good question! This is really quite confusing but the ont- prefix doesn't always mark the opposite meaning. It can also mean that something's beginning to do something (eg. ontvlammen, ontstaan, ontdooien, ontbijten, ...). So strictly speaking you could say that roeren literally means 'to move' and ontroeren means more like 'to set in motion'. But in the figurative sense (which is mostly used today) both roerend and ontroerend practically mean the same thing emotionally moving. If there's a difference I would say 'roerend' will cause an emotion which is a stronger and has a more lasting impact.

It's a really good question. I've never even actively thought about it, but there's definitely a difference in meaning between 'die' en 'dat' in this context and it doesn't really have anything to do with gender of the thing referred to. 'Die' is used for a specific thing and 'dat' is used for a 'general' group/kind of things. In this context 'die' fits probably best. 'Die heeft ze nog niet.'='She doesn't have that one yet.' (she doesn't own the specific title so you can still use it as a gift). 'Dat' can also be used though in a slightly different context: 'Dat heeft ze nog niet.'='She doesn't have such a thing yet.' (it is a book about a certain subject, say fishing, and she doesn't have any books about fishing yet).

It sounds unnatural indeed. 'Uit de grond' already sounds a lot better than 'uit de aarde'. This is because grond is generally what is below our feet and 'aarde' is really the earth/material itself. Also I think 'halen' works better than 'nemen' here because that's focused on the movement and 'nemen' is more focused on the action of taking. So you could say 'een grondstof uit de grond halen' but even better would be to use the specialized word for this context 'ontginnen'.

If you use any in the meaning of 'no matter which' you can also use 'eender welke' to more closely translate the meaning. 'Eender welke kleur is oké.' However it's true that the semantically close 'elke' is used more often in this context than it is in English.

Herkomst is more of where or under which circumstances something or someone came about/formed/grew up, while 'ontstaan' is more of how or when something comes about. 'Oorsprong' is more of a general translation of 'origin' which can be used interchangeably, especially with 'herkomst', but also 'bron' (which is implies more causality between the origin and the current situation). Examples: The Origin of Species - Het Ontstaan der Soorten Country of origin - Land van herkomst/oorsprong Point (0,0) is called the origin - Punt (0,0) wordt de oorsprong genoemd Pandora's box was the source of all evil - De doos van Pandora was de bron/de oorsprong van al het kwaad