Otdfbt

Across:

1. URL for commercial clothes (7)

3. Steal each commodity (6)

5. One gut was queasy, you can stick it out (6)

7. Throw caution to the wind and sell art (7)

9. Endlessly care for vehicle (3)

10. March saint does prank next to Dad (7)

12. Martha upset by one missing end of race (8)

15. Loose way of communicating (5)

18. Public school at standardized test (4)

19. Mistake when supporters back university (5)

21. Warm states in south remove restriction (7)

22. Engage cross by odd knitted item (3,4)

23. Keats chewed meat (5)

24. Damp filling of Elmo is trouble (5)

26. Ag nerd spoiled plot (6)

27. Stalk life-saving cells (4)

29. Missouri raptors have wild hairdos (7)

33. Endlessly suave in the city (5)

34. Lead crazily right to Chicago planetarium (5)

35. I am in neither script of old movies (5)

36. Truth is 11-0 in morning (5)

38. Buried in stress, even though it's an inning for stretching (7)

41. I am not in Bulgarian city seat (4)

44. Former Astro chewed many, many bytes (6)

45. Evenly, Lear invites Bert's pal (5)

47. Broken pot just the start of big nerd (5)

49. Quick break if pot's tip is reversed (3,4)

50. Spy agency takes in double-crosser who swallowed ring in Eastern European country (7)

52. Sample first ingredients of tacos and salads tomorrow evening (5)

53. Zeus changed channel (4)

54. Hobbit woman in front of broken door (5)

56. Initially, cadets on loans used money brought in at university (8)

58. Garment unraveled at sewer (7)

59. Modern core of poem (3)

60. Spanish gold found around country of Disney town (7)

61. The worm heard argument (6)

62. Snake language (6)

63. Net vision heard Stack Exchange is one (7)

Down:

1. Ana enumerates out loud for therapists (8)

2. Improvised a skit for Alaska city (5)

4. Sharp raw noodles contain shrimp (5)

5. Crown heads of ten international and royal agents (5)

6. Bets around as monsters (6)

7. A mom sounds obvious (8)

8. Men gut fishy spice (6)

11. Disputed region is a loud type of sweater (7)

12. Dank smell in emu skins (4)

13. Unpredictable and held in computer memory (6)

14. Headless trout rule type of country music (6)

16. Crazy Alan raging for mathematical relaxation (10)

17. Cow shred blended into creamy soups (8)

20. At first, happy youth might not sing songs (5)

25. Washington city filled wrap before Massachusetts (6)

28. North side of Chicago suburb is Hansen (4)

30. Unthinking, foiled a wild theft (10)

31. This stump (6)

32. Rex posed inside convention (4)

34. Mountain roast spilled taco (2,6)

37. Bush Jr. will speed up endlessly while my guitar does this gently (5)

39. Clover sprinkled around fastening tape (6)

40. Child swirling in central point of whirlpool (3,3)

42. Release Han from climbing movie (4,4)

43. Leader of Nokia swears recklessly by solutions (7)

46. Mother drops down loudly for remainder of division (6)

47. Info shattered a bit (4)

48. Hunk of meat pie (8)

51. Insist weirdly as rest (6)

55. No bumble bees are fat (5)

56. Rookie jazz player around Delaware (5)

57. Heartless mirage is wobbly in picture (5)

This is the first full cryptic I've written -- any feedback, good or bad, is appreciated!

Here's the completed grid:

And some comments, as requested.

Not bad at all, but I have a number of quibbles. Several "indirect anagrams" -- i.e., the answer, or a part of the answer, consists of an anagram of a word indicated only by a definition. That's generally viewed as Bad because there are just way too many possibilities. Some rather dodgy homophones; I particularly dislike 61a and 7d (though the latter might be partly a difference in accents). A few definitions aren't really definitions; e.g., "relaxation" doesn't define LAGRANGIAN; there is a mathematical technique called "Lagrangian relaxation" meaning relaxation of the Lagrangian, but "this word sometimes goes together with that word" does not a definition make :-). In general, the clues often feel too "straightforward" -- there's only one plausible way to parse them as crossword clues and/or the most obvious parsing of the surface reading is also the correct way to parse them as clues. On the other hand, the grid has rather little "checking" -- only a small fraction of the cells are shared between multiple clues. This means that if the solver gets stuck on one clue it can be very difficult to make progress -- and when some of the clues involve not-entirely-fair constructions like indirect anagrams, this is particularly irksome. (That was one reason why 61a annoyed me: it was a slightly iffy clue and its only interaction with the rest of the crossword was an E at the end of it.)

Credit where due:

I posted this with 10a, 18a, and 11d unsolved. OP kindly gave me a nudge (well, a shove) for 18a, which was enough to get the others -- though as it happens El-Guest also solved 10a about 30 seconds before I did :-).

Partial

Across

62) snake language (6)

PYTHON (programming language)

Combination of answers with credits

Across

9) Endlessly care for vehicle (3)

CAR [care - e, def: vehicle]

62) snake language (6)

PYTHON [double def.] @Tojrah

Down

20) At first, happy youth might not sing songs (5)

HYMNS [(h)appy (y)outh (m)ight (n)ot (s)ing, def: songs]

51. Insist weirdly as rest (6)
    
    

    
    

    ASSERT [anagram of AS REST]