To The Esteemed Miss Jacqueline Woo, Will You Be My Valentine?

Puzzle 1: Solve the Riddle

I have keys but no locks,
I have space but no room,
You can enter, but you can’t go outside.
What am I?

Puzzle 2: Unscramble the Letters

Unscramble the letters to reveal my secret word:

E, V, T, A, I, L, N, E

Puzzle 3: Solve the Number Patterns

Puzzle A: Find the next number in the sequence:
1, 4, 10, 20, 35, ?

Puzzle B: Find the next number in the sequence:
2, 3, 5, 9, 17, ?

Jacqui, Will You Be My Valentine?