SUPER STRENGTH
When this character moves due to its own action, it may either pick up an object or place an object it is holding. The object must be picked up from or placed in either a square the character occupies or an adjacent square. If this power is lost or countered while this character is holding an object, immediately place the object in the square this character occupies.

Question:
1) I has told that you can not pick up an object when doing charge if it is adjacent to an opposing character, Is that correct?

2014 rulebook page 16:

If entering that square
requires that the character end its movement, it can’t
pick up an object adjacent to that square

There's no clear yes/no answer to your question. It depends on whether or not your character has to end his movement when coming adjacent to the opposing character.

Also, "adjacent to an opposing character" might mean this:
. . .
. E O
. x .
. x .

or this:

. . .
. E .
. x O
. x .

(E = enemy, O = object, x = path of Charging character that has no means of ignoring other characters for movement)

In the first example you could not pick up the object, in the second you could. So, the object being adjacent to an opposing character has nothing to do with can you pick up an object or not.

What you need to think is does moving adjacent to the object force your character to stop. If it does, you can't pick up the object.

HYPERSONIC SPEED
Give this character a power action and move it up to its speed value; it adds 2 to its d6 roll when breaking away and May move through squares adjacent to opposing characters, but still needs to break away normally. During this move, this character may, as a free action, make one close combat or ranged combat attack with its range value halved for the attack. This character must be in a square where it could legally end its move in order to make the attack.

Thanks for the help. Know I understand it for charge.

2)In the case of Hypersonic Speed, the Character is continuously moving he never stops, until he has finished moving up to its speed value.

In your example
"adjacent to an opposing character" might mean this:
. . .
. E O
. x .
. x .

(E = enemy, O = object, x = path of Charging character that has no means of ignoring other characters for movement)

In this example could you pick up the object and use it for a close combat attack? or would you need to do a maneuver like the following:

. . .
. E O
. x x
. x .

to be able to pick up the object and then do the close combat attack?

(I edited your quote to number the path I think you mean.)
Either way would work as HSS lets you not have to stop when becoming adjacent.
It is important to note that in that other path you listed that you become just as adjacent to the enemy when you move to 2 as you would become moving directly from 1 to 3.

So, please confirm,

The close combat attack with the object would be allowed in the first example:

. . .
. E O
. x .
. x .

if by moving adjacent to the object the Hypersonic Speed (HS) character is not forced to stop, Right? So, the HS Character needs to be able to move after the close combat attack to be able to do it, or is the movement after the attack not necessary?

Generally, a character using HSS doesn't need to stop when it becomes adjacent to an opposing character. Correct.

The attack granted via HSS occurs *DURING* the movement; there is no before and after. So either the character is moving (and can attack) or it isn't moving (and can't).

And, if it is moving and attacking, it can pick up an object.

Thanks, for clarifying.

Is this power now an either/or?

Meaning, I cannot drop an object, move away and grab another? It's either drop or pick?

"When this character moves due to its own action, it may either pick up an object or place an object it is holding."

Yup, one or the other.

The dumpster weeps.

Great, thanks!