1. Taking the keys out of his pocket, he opened the door.
2. He took the keys out of his pocket then opening the door.
Are these 2 sentences different and if sentence 2 have wrong grammar?

Question

1. Taking the keys out of his pocket, he opened the door.
2. He took the keys out of his pocket then opening the door.
 Are these 2 sentences different and if sentence 2 have wrong grammar?

Answer

2. should be:

He took the keys out of his pocket then opened the door. - you should use past simple to show that one action followed another

The first one is a bit strange. It would mean that he opened the door at the same time as he was taking his keys out of his pocket. So the two actions weren't connected.

If you want to say that he used the keys to open the door, you need to use a perfect participle clause:

Having taken his keys out of his pocket, he opened the door.

The 'having' tells us that this action happened before the other one.

Entering the room, I noticed that the window was open. - I noticed this at the same time as I was going into the room.

Having entered the room, I noticed that the window was open. - I noticed this after I had entered the room.

Answer

2 is wrong. 1 is imprecise if you mean that he opened the door using the keys because the two events don’t happen at the same time. But it is the kind of thing that a native speaker might say.

Taking his keys out of his pocket, he noticed that his wallet was gone. (This is a correct example of the construction. The two events happen at the same time.)

He took his keys out of his pocket and opened the door. (Natural)

Answer

#1 is a perfect sentence.  By placing the adjective phrase, "taking the keys out of his pocket", directly next to the noun that it modifies ("he"), it achieves maximum clarity.

#2 is a bad sentence.  The adjective phrase "opening the door" is placed next to a noun, "pocket" that it does not modify.  The pocket is not opening the door.  In addition to that small problem, there is also a huge problem. The really bad mistake in #2 is that it attempts to use "opening" as if it were a verb.  "Opening" is an adjective, not a verb.  As a present participle, "opening" can have an object ("door") but it cannot have a subject.  It is not permissible to say "He opening the door".  A verb is needed ("opened").  You also need either a conjunction or a comma:

"He took the keys out of his pocket, then opened the door."
"He took the keys out of his pocket and then opened the door."