Solution:

3 and 7

Explanation:
Painters 3 and 7 are the only painters that match all nine circled areas.

Solution:

Six item that does not belong to this era are :
1. Plane
2. Table lamp.
3. Scooter.
4. Sunglasses.
5. Earphones
6. Mobile phone.

Solution:

797

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

Solution:

The sleeping baby is marked in the picture below.

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:

89

Explanation:
(1st-column-number * 2nd-column-number) + (1st-column-number + 2nd-column-number) = 3rd column number.

i.e

(3 x 1) + (3 + 1) = 3 + 4 => 7
(6 x 4) + (6 + 4) = 24 + 10 => 34
(8 x 7) + (8 + 7) = 56 + 15 => 71
(9 x 8) + (9 + 8) = 72 + 17 => 89

Solution:

FUCK

Explanation:
IF sound like the letter 'F'
YOU sound like the letter 'U',
SEE sound like the letter 'C',
KAY sound like the letter 'K'.

It's a clever way to use word fuck and it does not get blocked by filters.

Solution:

Tug of War

Solution:

3rd.

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

Solution:

There are probably many, many solutions, five such solutions are:
> √(7^6) - 3^5
> (57 + 3)/.6
> ((3!)!- 5!)/(6 mod 7)
> floor(3*5*6.7)
> ceil(357 * sin (-6))