Let's break this down.

The first sentence says:

For an obscure poet to have penned such a refined, poignant sonnet is not at all ________ .

The next sentence explains:
The sonnet has been a favored form for hundreds of years among both amateurs and famous poets.

So the idea is: it's not surprising that an obscure poet could write a great sonnet, because many people have used the form.
We need a word meaning "surprising" or "hard to believe" for blank (i).
- A. rare - doesn't fit idiomatically: "not at all rare" would mean "common," but the structure "For X to have happened is not at all rare" is possible, though "rare" is more about frequency than plausibility; but here the sense is about being puzzling or inexplicable.
- B. puzzling - fits: "not at all puzzling" = "not surprising."
- C. conceivable - "not at all conceivable" = "impossible," which is opposite of the intended meaning.

So blank (i) = B. puzzling.

Second blank:

I would be ________ , on the other hand, had not one, out of the sheer number produced during this time, surpassed Shakespeare on a bad day.

Meaning: given the huge number of sonnets written over centuries, it would be surprising if none were better than Shakespeare on a bad day. So "I would be surprised" if that hadn't happened.

Look at options:
- D. confounded - means bewildered, surprised (fits).
- E. vindicated - means justified, doesn't fit.
- F. hard-pressed - "I would be hard-pressed" means "I would have difficulty," e.g., "I'd be hardpressed to believe it" - but here the structure is "I would be hard-pressed had not one..." - not quite right; "confounded" is more direct for "surprised/astonished."

Between D and F, "confounded" fits the tone of intellectual surprise better.

Final answer:
Blank (i): B. puzzling
Blank (ii): D. confounded