Such a lovely idea

This sounds much more like an unusual building compared with the others, which (within limits) are probably fairly conventional.

Answer 2 is almost certainly best here.
Answer 1 suggests laughter: the style of the building might well have been in almost comic contrast to others already there, but this by nature doesn't seem a suitably serious form of criticism.
Answer 3 fails because 'quite' is (unfortunately, and unhelpfully) ambiguous: do we mean 'rather/somewhat out of keeping', or 'completely'?
Answer 4 is good because 'utterly', by original definition, suggests that nothing else could be any less compatible. But it lacks the emotive impact of 'monstrous', which suggests not only the huge size but also an aesthetic ugliness, or at best a lack of sensitivity (i.e. the plan, if built, would result in a vast ugly structure that would spoil the whole look and proportion of the area).

Answer 3 is much less mild than the others. The British have somehow acquired a reputation for being people who don't like to complain, but in the situation of Answer 3 it sounds as though the villagers would have specific objections which they might bother to raise. In the other cases the feeling is not strong or focused enough. The villagers might perhaps express their dismay ~ at least, to start with ~ in terms of being 'a little / slightly / somewhat / (etc) disturbed', but what they'd actually mean would be that it really did quite bother them. Meanwhile 'distinctly' is definitely the clearest option!

Whatever the news or discovery were, clearly the actual 'content' came as a surprise; but 'astounding' is the strongest of these four terms.

Most, if not all, of these verbs are 'wild-animal metaphors'. Snarling and growling both suggest that the animal's mouth is partly closed, or at least certainly not wide open, giving a sense that not all the power is yet on display. The 'roar' in Answer 4 is a total and unhesitating noise!
A 'purr' meanwhile may be a very good sign of power waiting to be unleashed; but if that's all the motor can manage at full throttle, this is either an underpowered car or it has an immensely sophisticated silencing system!

The outer two Answers (1 & 4) are too strongly positive in these circumstances, and No.3 doesn't really work ('fairly' rather undermines the excitement, and 'gives the game away'.) So Answer 2 is probably safest.

Most of the other Answers are really only about how genuine these people looked onscreen (e.g. in terms of their behaviour, 'period' faces/makeup/hair/costumes etc.); but 'convincing' suggests that we have identified with the deeper motives and actions as characters (e.g. that we felt a surprising sympathy for someone who at first glance might have seemed unlikeable, such as a drunk and/or murderer ... a 'beauty that lay deeper than the skin' in this essentially visual medium).

Answer 1 is just about the mildest way of trying to put across the idea that someone has (perhaps) mental problems and/or character flaws. The others are all more 'pointed'.

These are all quite good strong words, but 'nauseating' carries a clearer and more powerful medical sense of the physical symptoms that the food provokes, i.e. nausea (a feeling of faintness, coupled with a rapidly increasing likelihood of actually being sick).

The top three Answers are each weakened by (presumably unintended) puns:
'Deeply doubtful' (Answer 1) suggests that some people were scared at the thought of underground engineering, perhaps because they were claustrophobic.
'Wholly' (in Answer 2) sounds like a pun on 'whole' (i.e. they felt there was no need for anyone to go digging a hole).
'Bored' (Answer 3) suggests the other meaning of the verb, to do with the boring of holes.
None of these is seriously helpful, even if it may have been true; which leaves Answer 4 as the best, even if less punchily expressed.