Why do the police suspect Jack Reacher for Sandy's murder?

Why does Jack go to the place where Sandy is killed ( outside her apartment?)?

This is the source of your confusion....

Jack is going back to his motel...Sandy was killed outside her apartment and dumped behind Jack's motel.

Where Sandy was killed...

Where she was dumped (note the front of the building in the right side of the image)...

Here's an image from an establishing shot of the motel earlier in the movie...you can see the dump area indicated.

Why does he show up there just after the police arrives?

See above....he was headed back to his base...he had no idea the police would be there.

Here's Emerson exiting the building...see the name on the door? It's the same door that's open in the image above...

And who did the landlady think was the guy "who could kill her with one punch" ( in response to Emerson's question)?

Obviously, Jack...he doesn't stay under his own name, he was using the alias Ernie Johnson ^*

Clearly she thinks he could kill someone with one punch.

^{* Reacher uses Yankees second basemen as aliases}

And why do the police suspect him?

Let's see:

• He was involved in violent altercation with the girl's boyfriend only hours before.

• He tracks her down at work and confronts her.

• Her body is found behind his motel.

• He shows up in her boyfriend's known associates car at the place the body was found.