High German and Low German is a bit difficult.
In laymen terms and daily use "High German" is the "Dialect" that is talked in schools, used on radio and TV and is the modern "written german". It is in our days not really the "upper class" german but statistically lower class people tend to speak 'Dialect' only more often. While more 'upper class' people usually speak 'High German' only. However many people speak both, their 'Home Dialect' and 'High German'. I only speak 'High German' but I guess that is because I spend my time in school from 5th grade on in a gymnasium where most teachers spoke 'High German' and the kids came from 3 different majour dialects. Well, this particular dialect we now call 'High German' is a slightly evolved 'Dialect' (like all the other dialects, it is just a dialect, nothing 'higher' than the 'lower' ones). It is the dialect that is spoken or was spoken in the Area of Muenster. It became 'High German' that means distributed over whole germany and slowly adapted by higher classes because Martin Luther wrote his german translation of The Bible in that 'Dialect', and coincidently :D Johannes Gutenberg printed and distributed it widely.
Linguistic however the distinction is between the lower lands and is called 'Niederdeutsch' (roughly translated into 'Low' or more precisely 'Lower' german) and the higher lands. However that is as many 'Linguistic Classifications' just an arbitrary and very misleading one. At least we can says that all the dialects spread over the 'Higher Grounds' not necessarily have much in common, same for the dialects spread over the lower areas or the coasts. Or more precisely, coastal dialects amoung each other have much in common but not much with the dialects spoken in the non costal lower grounds, like in Niedersachsen (Lower Saxonia) or Nordrheinwestfalen (North Rhine-Westphalia). In other words I bet that modern 'High German' is according to the linguists more likely a 'Lower German Dialect' as it comes from the lower plains in the north-west of germany.
Beyond that, you'd need to ask a linguist. Over time, what you grew up hearing and saying defines how you say it, and what you can say. I strongly suspect there are some sounds that some people simply cannot make if they didn't learn early enough.
Yeah, we germans tend to mispronounce 'th' with a 'z' ... it is very difficult to correctly learn english (or any other weird language, like french or gallic) because you hear yourself different than others, when your teacher repeats 100 times 'what' you should say instead of mimiking what you 'actually sound' like you have hard chances. Most teachers are simply incompetent ... one even drove me to tears because he let me repeat stuff hours long instead of once explaining me what I actually do wrong.
On the other hand, try chinese ... they basically sing. And that in a way which is nearly not hearable for many europeans. The syllable 'shi' can have many meanings depending if the 'i' is simply pronounced, or prolonged or is going up in tune or down ... well perhaps 'shi' is a bad example, I don't speak chinese. Luckily japanese is super simple :D. Except for the unknown words it sounds like german or italian, clear vowels more or less written like you speak it (or other way around: spoken like it is written)
The longer I live, and the more non-native speakers of English I meet, the more I have a hard time explaining all of the corner cases in English, because it's made up of stuff from so many different languages.
Ofc, the british islands got invaded a couple of hundred times. Many invaders who stayed, got half assimilated and half they conquered a little kingdom for themselves. When the next wave of invaders came they fought with the older residential tribes together against the new invaders ... but again some of the new ones managed to settle ... so many languages got melted into english.