You are punished for changing the game time (no matter how much, it seems), but not the system time. Here's what happens:
If you change the time on your 3DS system, Animal Crossing seems to simply think that's the time it is now. Trees grow, events change, the only "bad" things that happen would have happened with the flow of time. Even going back in time via this method seems to work okay, even when going to a day previously played.
If you change the game time, using the option at the main menu of Animal Crossing, you will randomly trip for a while after changing the clock. The duration of tripping seems to last longer than the current play session, possibly the full day? But it eventually goes away. If, however, you were to change the game time this way before every play session you would trip randomly every single session, which is highly frustrating.
Also note that going backwards in time will spoil any turnips you had, since the game knows you went backwards, while it doesn't know you went forwards if you go by the system clock.
tl;dr: Change your 3DS's system time to time travel, do not mess with the in-game clock regularly or will will randomly trip.
The tickets are not random, so your latter assumption is correct. The numbers are predetermined and will give you a certain prize based on which number you had. There are a few numbers (4, 6, 16, 30, 38) which will only give you a random piece of regular furniture, carpet or wallpaper rather than one of the unique items.
The full list is as follows:
1. Mushroom Mural
2. Block Floor
3. Hero's Tunic
4. Random "regular" furniture, wallpaper, or carpet
5. Hero's Pants
6. Random "regular" furniture, wallpaper, or carpet
7. Peach's Parasol
8. Hero's Cap
9. Majora's Mask
10. Samus Mask
11. Midna's Mask
12. Toad Hat
13. Red Pikmin Hat
14. Blue Pikmin Hat
15. Yellow Pikmin Hat
16. Random "regular" furniture, wallpaper, or carpet
17. Brick Block
18. Coin
19. Flagpole
20. Fire Flower
21. Super Mushroom
22. Koopa Shell
23. Starman
24. 1-Up Mushroom
25. ? Block
26. Green Pipe
27. Fire Bar
28. Cannon
29. Yoshi's Egg
30. Random "regular" furniture, wallpaper, or carpet
31. Triple Shells
32. Kart
33. (Pikmin)
34. Blue Falcon
35. Master Sword
36. Arwing
37. Triforce
38. Random "regular" furniture, wallpaper, or carpet
39. Dolphin
40. Virtual Boy
41. Wii Balance Board
42. Varia Suit Pants
43. Varia Suit Shoes
44. Bad Bro 'Stache
45. Big Bro Mustache
46. Varia Suit Body
47. Metroid
48. Triple Bananas
49. Hero's Boots
50. Fay's Mask
-Source
Best Answer
Yes, they can appear in the same week. They can't appear on the same day, though.
Well, there is a way to have both of them at once. Katrina, the fortune teller, opens a store in your Main Street. Then, she no longer needs your tent. Redd can show up then and Katrina will also be in your town. Technically.
However, if they're both in tents... the two tents use the same "space" so they don't appear together. (Both tents appear in the town square.) So only one can appear at a time. Redd is more likely to show than Katrina, who is not guaranteed to show every week. Redd shows up once a week, so you should see him every week without fail. That means Katrina always shows up in the same week as Redd.