Why is the "current time indicator" highlighted with a semi-transparent border on the right?

The semi-transparent area indicates Shutter Phase. The normal composition settings for shutter angle are 180º to mimic a standard Cine shutter and -90º to calculate motion blur starting in the horizontal middle of the comp frame. This emulates the motion blur you get on a standard cine camera. It looks like your Comps Advanced settings have an Offset of 0º, and I am guessing an Angle of 360º. This will give you more than the standard amount of motion blur.

Setting the Shutter Angle and Offset is critical if you are trying to match motion blur in your source footage. You can find the exposure time and frame rate in the metadata of some footage. The info in the Project Panel only shows frame rate, duration, and codec.

After Effects trims layers and sets keyframes at the beginning of the last frame. If you want a layer to end at a specific frame, you need to set the Out Point one frame before the desired ending time. This is standard behavior for animation and compositing apps.

If the Shutter Phase indicator bothers you, zoom out of the timeline a bit.

Cause it is indicating the this is the frame it is reading. Playhead always previews the frame on the right.