Native speaker here – American English (New England, Boston area).
I may be grasping at phantoms here, but I have a very faint impression that when one uses "would always", it implies "on those occasions on which that person would do this thing, they always elected to do it in the following way", while, in contrast, "was always" implies that the person (or thing) so described was multiplying occasions to do the thing.
That is, using your examples,
She would always send me strange birthday gifts.
Suggests to me that on the occasion of your birthday, she could be relied upon to choose gifts that were strange, while
She was always sending me strange birthday gifts.
would suggest that she wasn't waiting for your birthday to send those strange dirthday gifts!
Likewise,
Sam and Mary would always choose the most exotic vacation destinations.
suggests that Sam and Mary's vacation destination choices were consistently exotic, while
Sam and Mary were always choosing the most exotic vacation destinations.
suggests that Sam and Mary have a very, very busy vacation calendar.
This
Ned would always show up at our house without calling first.
suggests that it was Ned's custom to drop by without calling first, while
Ned was always showing up at our house without calling first.
suggests Ned is making a serious nuisance of himself by imposing on us so very frequently. (Note that in this example, the "was always" formulation has a much strong negative valence than the comparative "would always.)
The difference, I think, is that used this was "was always" is hyperbole, while "would always" is merely a generalization.
Your description of "was always" + verb as implying a negative is correct, but it doesn't explain how that works. It is using hyperbole, which is a figure of speech which conveys valence by exaggeration. When someone says of someone "he was always doing that thing!" it is not usually meant literally; it is meant as exaggeration for effect.
In contrast, "would always" may well be meant literally, or close to literally. When somebody says "he would always do that thing!" they may well mean "whenever he did a thing, it would be that thing!"
By way of illustration: I had a friend who would always be late to parties. Famously so. Like, numerous times he arrived at parties when the last of the rest of the guests were saying good-bye to the hosts. Once, story has it, he showed up the day after the party. Yet I wouldn't say of him that he was always being late to parties because he didn't go to parties all that often. It wasn't like his life was full of party-going, only late. But, by gum, when he went to parties, he would be late; you could bank on it. So my saying of him that he would always be late to parties was perfectly, incontestably, literally true.
Being jealous is what's called a free adjunct. It would be very difficult to explain exactly what linguists understand about it to you, since it requires a lot of technical knowledge.
The best way to explain it is this. Let's start with the sentence:
Mona didn't let her boyfriend dance with any of the cheerleaders.
At this point, the listeners doesn't know why Mona didn't let her boyfriend dance with any of the cheerleaders. However, the speaker wants to let the listener know why Mona didn't let him, so they want to add that Mona was jealous.
The most straight-forward solution would be your sentence,
Mona didn't let her boyfriend dance with any of the cheerleaders because she was jealous.
The reverse also works (Because...Mona...). But they require two clauses inside the main sentence.
[[Mona didn't let her boyfriend dance with any of the cheerleaders] [because she was jealous.]]
Instead of having to put two clauses inside the main sentence, why not just have one with some extra information tacked on?
[Being jealous,] [[Mona didn't let her boyfriend dance with any of the cheerleaders.]]
This is analogous to:
Jealously, Mona didn't let her boyfriend dance with any of the cheerleaders.
The difference is that with jealously, it moved from the main clause to outside it. In other words, the original sentence was:
Mona jealously didn't let her boyfriend dance with any of the cheerleaders.
And then the jealously moved in a process we call topicalization. Topicalization in English moves parts of the sentence to the front so they're more prominent.
↓----------¬
Mona jealously didn't let her boyfriend dance with any of the cheerleaders.
With being jealous, however, it didn't move from anywhere. The speaker just thought of it and attached it to a point where it's allowed, which includes the front of the sentence.
Being jealous
↓
Mona didn't let her boyfriend dance with any of the cheerleaders.
In conclusion, being jealous is basically a quick way of saying "Mona was jealous, therefore...." with fewer words.
Best Answer
"Pleased with" and "tired of" are unambiguously correct.
"Surprised at" is also correct, but in American English it sounds a little clunky. In a sentence like yours above, I would usually choose "by": "...but everybody was surprised by her attitude."
One weird quirk with the word "surprised" is the change in meaning when the object of the preposition is a person. Consider:
This indicates that Samantha surprised Julie on purpose somehow, like by hiding behind the curtains for a surprise party, or sending her an unexpected gift.
This indicates that Samantha behaved in a way that Julie hadn't anticipated. Samantha wasn't behaving with Julie in mind; she just acted, but her behavior surprised Julie.
That is just a weird distinction with people, though. For the most part, you can use "at" and "by" interchangeably with "surprised" and people will get your meaning without much trouble.