Dear Solver,
Today I went to 4A, which is not short of wonders regardless of its small size. After staying at its capital, 23A, I went to view nature in a protected area, where I saw Mount 13A-34D from afar, and in contrast got to take a close look at the 36A 1A. Afterward, I went to the 16A 22A and the 27A 29A 32A 33A. These are significant as they are the remains of sites which would still have been standing today, had volcanoes not ravaged the land. And now that I think about it, its volcanic background seems to be the reason for its epithet.
The people here are descended from ancestors that arrived from the nearby larger island. At present, they celebrate in a festival the harvest of a fruit, the 14A, and this occurs in the last quarter of the year. Though this may not be important, I feel the need to clarify that the name of the fruit as used in the name of the festival is considered plural form in English.
Where am I? Good luck!
P.S. All missing entries above can be found on the Wikipedia page of 4A. However, only 4A, 23A, 14A and 13A-34D have their own Wikipedia pages, and the title of the Wikipedia page of 14A is its scientific name.
P.P.S. For convenience, here is a Penpa link in which the crossword can be solved. Make sure to enter the answers in all-caps and in either green, blue or red color so that the crossword checker works!
Across
1. (See 36 Across)
4. Photographer, one that can shoot with me in tropical island (8)
10. Ensure no kid gets fungus (5)
11. Weekday is occupied by class in a twist - thanks, it's hideous (11)
12. As mentioned, carp is shy (3)
13/34D. Volcano born with high and low temperature extreme all around, repeatedly recorded (5-5)
14. Unprotected plant sector mostly yielding fruit (6)
16. Immersed in star knowledge (6)
18. High belter! (6)
19. Partners help us now (3)
22. Some very cold water out of current dispenser at yard where one may rest (8)
23. Snake indeed not inside capital (8)
27. Long-lasting illness with forgotten origin (3)
29. Take note to divide gift, a French sweet (6)
30. Figure, say, about university (6)
32. Incomplete way to make butter, tea, bread and wine may be mentioned here (6)
33. Mars rover ultimately not held by America (5)
34. Go to beat a famous song (3)
36/1. Flowing water in a flask at lab was spilled (11 5)
37. See me by Earl regularly carrying hot coal (5)
38. Guitarist and singer served partially as substitutes (6 2)
39. Request taken the wrong way: you and I turned to one side (5)
Down
1. Mural technique failing forces fellow to hide a short while (6 5)
2. Look at Spanish and Italian river changing course - insane (5)
3. Small, having the smallest amount! (9)
4. Get hail through (4 2)
5. Writing in a mixture of ink some names (8)
6. Had lunch perhaps behind grand door (4)
7. Outrageous lie as to how disease may be stopped? (7)
8. Makes foam for sleep in returned empty space provided (6)
9. City - one missing it kind of blue (4)
15. Question bad smell in disguised warship (1-4)
17. Pay it no heed, Nevada man. (3, abbr.)
20. Short distance to home shrouded in silence - move forth in the waters (5'1 5)
21. Friend, new times are here in New York City area (5)
24. Woman seen during wash by leader, one beginning adultery! (9)
25. Spray flyer black (3)
26. Sirs out, with time to travel around?! (8)
28. Had relatives and is intimidating (6)
29. Spoke ill of support piece (7)
31. Essential wood component in inner covering (ending at a higher level) (6)
32. About a half-joke: it may have layers (4)
34. (See 13 Across)
35. Sibling takes first victory (4)