The solutions are shown below.

Move the minus sign to the top of the second vertical line to get “10 to 10”, i.e. 9:50.

The vocalist’s name is Tessa. On her notebook it is written “I’m diving into the DARK gloom End to start“. On the poster in the top right corner it is written DARK and underneath ASSET. “Asset” spelled backwards becomes TESSA.
The bassist’s name is Delilah. Her shirt features a cat, which is also present on the Freddy Mercury poster. The lyrics written on it are from the song “Delilah” by Queen.
The drummer’s name is Lisa. Inside her backpack there is a copy of the book “1984” by G. Orwell. On her backpack there is a sticker which also appears on the poster behind Delilah. The poster says “Local punk’o’matIc AnarchiSts bazAr”. If one selects the 1st, the 9th, the 8th, and the 4th letters from each word, the resulting name is LISA.

We color the vertices in five colors as shown in the image below, such that each face of the dodecahedron has 1 vertex of each color. Then, the sum of the four numbers from each color must be equal to the sum of all numbers written on the faces: 1 + 2 + … + 12 = 78.
If 16 of the vertices have the same number written on them, then by the pigeonhole principle there will be 4 vertices with identical colors and identical numbers. Since 78 is not divisible by 4, we conclude that this is impossible.

The least number of moves required to switch the positions of the knights is 16. An example is shown below.
Next, we prove that it is impossible to switch the positions of the knights with less than 16 moves. Since the white knights occupy 2 black and 1 white squares, they need to end up on 2 white and 1 black squares, and each knight must make at least 2 moves in order to get to the opposite side, the total number of moves for the white knights should be an odd number, larger or equal to 2+2+2=6. The same applies to the total number of moves for the black knights. Therefore, the only possible way to get a total number of moves less than 16 is if both the white knights and the black knights move exactly 7 times.
We assume it is possible to switch the positions with 7+7=14 moves in total. Then, the white knight on A2 and one of the white knights on A1, A3 should make 2 moves each, and the third white knight should make 3 moves and land on a white square, either D1 or D3. Without loss of generality, we assume the knight on A1 makes 3 moves: A1-B3-C1-D3. Then, the knight on A2 should make 2 moves: A2-C3-D1, and the knight on A3 should make 2 moves: A3-B1-D2.
We make the same argument for the black knights. Since it is impossible that the white knight on A1 moves along the trajectory A1-B3-C1-D3 and also the black knight on D3 moves along the trajectory D3-C1-B3-A1, we conclude that the black knight on D1 should make 3 moves: D1-C3-B1-A3, the black knight on D2 should make 2 moves: D2-B3-A1, and the black knight on D3 should make 2 moves: D3-C1-A2.
This is only possible if:
the knight on A1 moves to C1 after the knight on D3 moves to A2
the knight on D3 moves to A2 after the knight on A2 moves to C3
the knight on A2 moves to C3 after the knight on D1 moves to B1
the knight on D1 moves to B1 after the knight on A3 moves to D2
the knight on A3 moves to D2 after the knight on D2 moves to B3
the knight on D2 moves to B3 after the knight on A1 moves to C1
We get a contradiction which means that the least number of moves is 16.

Blood is thicker than water.
Home is where the heart is.
It takes two to tango.
Haste makes waste.

You should fill the words FIVE, THREE, FOUR to get:
“In this shoe, there are five H’s, three O’s, and four T’s.”

The front wheels of the bicycle are traveling more distance and making sharper turns. Thus, the red tracks (as shown on the image below) correspond to the front wheel, and the green tracks correspond to the back wheel.
Then, since the back wheel is always pointing towards the front wheel, we conclude that the bicycle is moving towards the right.

No use over spilled milk.
Two wrongs don’t make a right.
The squeaky wheel gets the grease.
When there is a will, there’s a way.

A piece of cake
An ace up one’s sleeve
Big cheese
Play one’s cards close to one’s chest
Cats got your tongue
Cherry on the cake
Crow over
Cut the chase
Don’t put all your eggs in one basket
Hit the nail on the head
Have (one’s) plate full
Heart on one’s sleeve
Holding a cat by the tail
In a nutshell
Kick the bucket
Make ends meet
Picture is worth a thousand words
Joker in the pack
Put a bug in someone’s ear
Put one’s best foot forward
Red herring
Silver spoon in your mouth
Spill the beans
Tie in knots
The shoe is on the other foot
Time flies
You can’t make an omelette without breaking egg