Solution:

A B C
E F G H
I J K L
M N O P
R S T
5 horizontal rows
4 vertical columns
4 diagonals with slope 1 (ROL, NKH, MJG, IFC)
4 diagonals with slope -1 (SNI, TOJE, PKFA, LGB)
2 knight's move diagonals with slope -2 (AJS, BKT)

Solution:

Initially, there are only two apples on the tree. I got one apple using the slingshot and therefore now one apple is on a tree and one with me.

Note: We got one apple(not apples).

Solution:

In the corners of the square, tighten two ropes. Tighten another rope between them by putting rings on each rope. That rope should be tightened on the sheep's neck on the other end.

Solution:

Watermelon

Explanation:
- Something their friend Howard can eat: watermelon
- Something their neighbor penny can drink: juice of watermelon
- Something their friend Raj's cow can eat: Watermelon rinds
- Something his girlfriend Amy can plant in her garden: the seeds of a watermelon

Solution:

The fastest or even the slowest rabbit can only run till the mid point into the given garden. After the mid point, it will actually be running out of the given garden.