Quoted from the first page -- I am answering using mostly NFHS rules

Offense:
1.How much bumping is allowed by the offense? Whether it's using shoulder or using their lower back (hip) to bump. Especially during post up & under the rim shots.

If a defender has Legal Guarding Position and the offensive player pushes him or displaces him from his spot on the floor, I have an offensive foul. If a post player and his defender are wrestling for position down low, I am closely watching for a holding or pushing foul, but usually let them play a little. Again, it depends on whether a player was put at an illegal disadvantage.

2.During post up or box out, how much arm is allowed to prevent the defender from getting close? Are you only allowed to use the arm to "block" or can you outright use your body weight on the arm and "push"?

If the offensive player is holding the defender away from him by using his arm, it is an offensive foul. If the defender is using his forearm in the offensive players back to push him or hold him where he is, it is a foul on the defender. Again, all depends on who is putting who at an illegal disadvantage.

3.What is "Up Down" rule, can you run the 2 steps in the mean time do fakes or you have to either pass or shoot once your arms in shooting form?

I am not familiar with the "Up down" rule? Perhaps you mean travelling, which is picking up your pivot foot and putting it down again before releasing a pass or shot. If a player has ended his dribble, he must either pass or shoot, to dribble again is a "double-dribble" violation.

4.How much space must a screener give to make the screen legal? And must you hold both hands at your crouch when screening? What if you just position your arms normally like when you standstill, can you hold your hands to the chest if you see the defender charging into you to protect your body?

A screener must give the defender ample time and distance to avoid the screen. While moving, the defender must be able to get out of the way, which depending on the speed of the defender, may be one or two steps. While the defender is stationary, I think the screen does not have to be set in consideration of time/distance. You may have to ask others or consult a rulebook for the requirements of a legal screen, but I think the arms should be within the body area, not sticking out to clip the screenee.

5a.If an offensive player runs in between a defender and ball handler is it consider a screen? Say if the player just "passing by". And would it be an illegal screen?

This would be an illegal screen if the defender was prevented from legal movement. There is a type of screen called the "brush screen" which dangerously skirts the line between legal and illegal. Again, was the defender put at an illegal disadvantage by this offensive player running through?

5b.If a offensive player runs infront a shooter & defender to block the defender's path how quickly must he gain position before being called illegal screen should contact made?

Again, judge by the time/distance given as well as the illegal advantage/disadvantage gained.

6.How does the 3second in the paint timer works? When does it reset? For example you post up in the paint, does it reset once you received the ball, or when you start the dribble, or when you catch the ball after dribble, does the counter still counts if you start doing pump fakes/pivot? When does the 3 second counter stop/reset while you are still in the paint? What if you end up passing the ball does the counter for that player gets reset?

I learned this the hard way, so I am glad you are asking.3 seconds exists so that an offensive player cannot camp out in the paint. If a player posts up, has been in the lane for 2 seconds, and receives the ball, we allow him a little extra time to make a move to shoot. If the post player, for example, received the pass at 2 seconds, kicks it out to re-post, and does not leave the paint, you should call 3 seconds. Dribbling or passing does not factor into the 3 seconds equation. However, 3 seconds resets on any shot attempt. If you work youth ball, you will hear many parents yelling for 3 seconds when shots and putback attempts are being missed with about 8 players in the lane. Ignore them. 3 seconds also resets on a change of possession. Also, 3 seconds only applies when the ball has froncourt status with team control.

7.5 seconds back to basket, how close do you need to be for the counter to start? under what condition does the counter reset (i.e fake half spin)? does it count when you are not dribbling but back to basket?

I believe this is only an NBA rule. Also known as the "Mark Jackson Rule". I don't know about this rule other than that.

10.Is it an offense if you throw a ball at the opponent with full force?

Perhaps it is just a turnover. If done maliciously, consider an intentional, flagrant, or flagrant technical foul. Remember, we are expected to know the rules, but we are paid for our judgement. I once had a player throw the ball in anger at his own teammate. The ball ricocheted off the teammate and out of bounds. Turnover. That player was promptly subbed.

Rebounding:
1.How much contact must be made before over the back foul applies? How to determine if a player is indeed infront?

There is no such thing as an "over-the-back foul". That is simply a layman's term. We officials call it a "pushing foul". Was the player in front put at a disadvantage? Did the player behind push the front player so he could grab the rebound and attempt a putback. If yes, call the push.

2.How much arm/elbow can you use while boxing out for rebound? And how much lower back (hip) bump can you use?

I think a proper box-out is mostly hip/butt. If a player backs out his man with his butt, I am unlikely to call a foul. Watch the arms though, there might be a hold on the player in front trying to prevent his man from running around him.

3.Are body contacts allowed during jumping for rebounding? Can you slap the opponents hand/arm while on air?

Again, read the NFHS (depending on what rule set you use) section on "Incidental Contact". Again, consider the advantage/disadvantage gained on the play. If the ball is loose, and two players are going vertically to secure the rebound, I am probably not calling a foul if they high-five.

4.Does shooting foul apply for immediate airborne rebound putbacks (grabs rebound and shoots before landing)?

If a player if fouled while shooting (gathered to some, act of shooting to others) it is a shooting foul. It is the same whether on a jump-shot or a putback attempt.

5.How much body contact is allowed for a chase for loose balls? Can i just charge towards the ball and knock the other chaser down if both are close?

This thread has a good discussion of whether or not to call a foul during a loose ball. In the video the officials did not call any fouls before the held ball occurred, but it could be argued that a foul was committed by one playing jumping on/falling over the other player.

That is all i can think of on top of my mind right now.

Also can someone explain the positions for throwing in out of bounds ball?

Check your officials manual.