Solution:

Seven

Explanation:
5(dead) + 1(Alive) + 1(you)

Solution:

7

Explanation:
Put batteries into 3 groups: two groups of 3 and one group of 2.
It guarantees at least one of the group has got two working battery
Group of 3 requires 3 attempts to verify if 2 batteries of the group are working (B1+B2, B2+B3, and B1+B3) while the group of 2 requires one attempt (B1+B2)
Total attempts = 3 + 3 + 1 = 7

Solution:

3

Explanation:
Note: Glass 5 6 and 7 not possible as there is a blocked connection.
Now, as the connection to 3 is lower than that of 2, it will fill first while rest beer glasses will remain empty.

Solution:

797

Explanation:
797 is a prime number
79 is a prime number
7 is a prime number

Solution:

==== 65 ==== 35 ====
== 34 === 31 === 4 ==
= 10 == 24 == 7 == -3 =

Solution:

8 Steps

Explanation:
Steps------2L Gallon-------5L Gallon
A-------------12-------------0
B-------------07-------------5
C-------------07-------------0
D-------------02-------------5
E-------------02-------------0
F-------------00-------------2
G-------------12-------------2
H-------------09-------------5

Solution:

Phoebe broke the machine and Monica is telling the truth.

> Rachel says Monica did it
If this is true, then the last statement must be true as well.

> Monica says Rachel is lying

> Phoebe says she did not.
If this is true, then one of the first two statements must be true as well.

Solution:

3rd.

Explanation:
Rule: Take the bottom row, flip it, and put it on the top.

Solution:

It can be done as shown below.

Solution:

As shown in solution picture, flip the first number and stack on the second number, you will get fish eight and triangle respectively.