If I can resurrect this one, I think I've spotted the links between all the previous partial solutions, worked out an element that had been missed by all, and can explain the additional hints in the text. Your girlfriend wants you to buy her:
Exploding Kittens, the card game
Puzzle 1 (solved by @PeregrineRook):
Is a Mastermind puzzle, which produces the answer TACO.
Puzzle 2 (solved by @ThirupathiThangavel):
Is a simple word puzzle, which produces the answer WATERMELON.
Puzzle 3 (worked on by @Techidiot with a comment that came very close from @GarethMcCaughan):
Part 1 actually translates via rot-1 as 'I am one thing made of many. I'm very manly but I prefer men.'
Part 2 translates via rot-25 as 'Whenever people discover me I always grow on them. If I become colorless, wisdom comes.'
These clues lead to the answer BEARD:
I am one thing made of many. - One beard is made of many hairs.
I'm very manly but I prefer men. - A beard is considered a manly thing to have; it 'prefers' men in the sense that it's usually men it grows on.
Whenever people discover me I always grow on them. - A beard quite literally grows on a person...
If I become colorless, wisdom comes. - Grey hair (or a grey beard) is a sign of age and 'wisdom comes with age'.
However, there was an extra clue hidden in the bold and italicised letters of Puzzle 3 which nobody spotted (because nobody was looking for it):
The letters produced by the rot operations on the bold letters give: AHYIRUPSD, which anagrams to 'HAIRY SPUD'. Since 'spud' is another word for 'potato' this leads to the answer HAIRY POTATO (don't see it yet? Bear with me!).
Meanwhile, the letters produced by the rot operations on the italicised letters give: EDNREREGRHI, which anagrams to 'RED HERRING' and has no further utility for the puzzle!
Why do these lead to the answer above? Because:
4 of the 5 types of 'cat card' in the original game are called TACOCAT (pleasingly palindromic), CATERMELON, BEARDCAT and HAIRY POTATO CAT.
There were other clues in the preamble too:
1. She's really lucky - Exploding Kittens game is partly a game of chance, in the way the deck is shuffled and hands are dealt.
2. She likes card and board games - It's a card game.
3. She likes animals (especially dogs and cats) - It's all about cats!
4. She had a cat named Ralph - The fifth 'cat card' in the game is called the RAINBOW RALPHING CAT.
5. Her favorite song is that double rainbow song - Again, as per 4.
The other answers between them each had one component of the final solution. Hopefully this finally now brings them all together in totality with the fourth previously unspotted one, and you can get down to the shops PRONTO! Here's hoping your girlfriend is a VERY patient woman ;-)