Time Remapping graph not looking right

You are looking at a speed graph. Look at a value graph and you will see what you expect. Remember, that is 'time' that you are looking at, not speed. The speed graph is going to show you how fast time changes. Here's what it looks like with show reference graph and edit value graph selected. The clip speeds up, then freezes for a few frames, then continues and slows to a stop at the end.

I believe you also have shown all keyframes selected.

it's normal, the dashed point mean that this part of time is set to the beginning or ending. so their are nothing to play is this time because you simply move the first and the last time remapping keyframe to the middle of your composition, the second dashed line i think it's the reference line or so.., you can click on (chose graph type and option) and remove the unwanted guid and line.