The use of 'Being' is not incorrect here, but you can't use it with 'precisely' in this way.
Being more precise, I just don't even know what "end up" means.
More precisely, I just don't even know what "end up" means.
Both of these sentences should be preceeded by something is vague, that needs a more accurate statement to follow it ...
As easy technique for checking this:
Take the original sentence: "Essos is an immense landmass located to the east of Westeros, extending into the far east of the known world."
And make the ing into a subject and verb phrase:
"Essos is an immense landmass located to the east of Westeros and it extends into the far east of the known world."
It describes ...
The sentences have adverbial phrases with present participles.
Such a phrase after the main clause can describe an additional action (often performed by the subject of the main clause, like in sentence 3), but not necessarily a simultaneous one. In sentence 1 the ...
To my understanding (different from what the comments say) here is what I believe being described.
a mattress is float in a pool (not spinning.) The wind is causing them to move in a circular path around the mattress, which leaves ripples in the water in a circle around the mattress.
This book was written in 1925, English has changed a lot since then, and ...
I'm afraid your prior assumption is incorrect. These are not "dangling participles". These are just ordinary participles.
Many participles, like those in (1-4), are formed from reducing relative clauses, like those in (1'-2'). They are not ungrammatical, and the participles in (1-2) are not "dangling". (3-4) are similar in structure, and there's nothing ...
The problem with your examples is that each of those inserted phrases ends with a noun which precedes a participle clause and can combine with it, giving some false sense. With such a word order, an additional comma just after the noun could prevent from reading like: 'tree waiting for me', 'my bed lying down' and 'the riverside whistling'.