1. What is the name of the normal language that character's speak? What are we hearing when we read the various Inquisition books?

Low Gothic (space English) is the language of the Imperium. High Gothic (space Latin) is sometimes used by the upper rungs of society, but it's mostly a ceremonial thing as I understand it.

Imperial Worlders and Highborn generally speak High Gothic only. Agri-worlders, hiver-worlders, etc generally speak low gothic. Low gothic is more common.

I like to think of high gothic like Old English. Think Downton Abby.

Low gothic is more like modern slang talk/street talk.

They are both basically the same language but it requires some training to speak one if you've grown up with the other.

Imperial Worlders and Highborn generally speak High Gothic only. Agri-worlders, hiver-worlders, etc generally speak low gothic. Low gothic is more common.

I like to think of high gothic like Old English. Think Downton Abby.

Low gothic is more like modern slang talk/street talk.

They are both basically the same language but it requires some training to speak one if you've grown up with the other.

No, sorry, that's not right. Low Gothic is the 'Common Tongue' of the Imperium; High Gothic is the official language of the Adeptus beaurocracies (yes, I know it's spelled wrong) and other elite organizations who need a more precise language to carry out their official functions (and, like Tom said, it is depicted as Latin in 40K fiction). Slang/street talk would be considered 'Hive Dialects' and would vary wildly from world to world.

I'll consider myself told!

Imperial Worlders and Highborn generally speak High Gothic only. Agri-worlders, hiver-worlders, etc generally speak low gothic. Low gothic is more common.

I like to think of high gothic like Old English. Think Downton Abby.

Low gothic is more like modern slang talk/street talk.

They are both basically the same language but it requires some training to speak one if you've grown up with the other.

No, sorry, that's not right. Low Gothic is the 'Common Tongue' of the Imperium; High Gothic is the official language of the Adeptus beaurocracies (yes, I know it's spelled wrong) and other elite organizations who need a more precise language to carry out their official functions (and, like Tom said, it is depicted as Latin in 40K fiction). Slang/street talk would be considered 'Hive Dialects' and would vary wildly from world to world.

This.

The Imperium operates with 3 categories of languages:

The vernacular languages. These are people's native languages. The Imperium likely has rather a lot of them. For reference, right now here on Earth we have around 6500 currently spoken languages, depending on your criteria.

Distinct languages tend to happen when distinct social groups exist for several generations.

In the Imperium, pretty much everywhere people live, they've been living for 1000+ years. So pretty much every place with any kind of native population, should have a native language.

Also, while practically everyone will have a vernacular language that isn't Low- or High-Gothic, Practically no one will share the language unless they grew up in the same community.

The lingua franca, or trade language. This is Low Gothic. Whether and to what extent people speak this, depends mostly on how educated they are and how much they need to be able to speak it to earn a living. Amusingly Latin is one of several such languages that has been used here on Earth. Present day English can also be considered such a language.

You'll have an easier time of playing the game if you assume everyone worth talking to speaks Low Gothic reasonably well. If verisimilitude is your thing, though, Low Gothic shouldn't really be one language, but rather an amalgam consisting of mostly equal parts High Gothic (Latin), Low Gothic (English) and whatever language or languages are spoken locally. The Low Gothic on one world should be barely understandable to Low Gothic speakers from another world.

The official language of the Imperium. This is High Gothic. This is pretty much only spoken by members of the Adepta, the social/political/economic elite, and whatever natives that has to work closely with such people. Knowledge destined off-world will usually be in High Gothic. High Gothic is widely considered fancy-pants, and someone who has no reason to be able to speak it can likely get in trouble for doing so. Neither the local elites nor the Adepta appreciate people eavesdropping or knowing too much, and the hidebound masses probably won't appreciate what they might easily consider a smart ass.

I'll consider myself told!

No worries- I've made plenty of mistakes on these Forums m'self...

Incidentally, the existence of a lingua franca presupposes a certain amount of contact and centralized communication. The evolution of modern languages along national lines tends to be closely associated with centralized distribution of information creating a standard of communication, i.e. the printing press producing newspapers with regular spelling habits or even more so radio/tv causing people to consider the dialect heard on the news to be correct and all others to be a variation and teaching such things in schools.

Thus, a planet cut off from regular contact should have fewer gothic speakers and more variations, as would outlying settlements on a planet even if it had more contact. A planet with regular contact with both the rest of the sector and the imperium at large, including a significant adeptus presence, would have more exposure and access to "proper" gothic both high and low and would consequently see more fluent speakers of both and less irregularity in their use of the languages.