Yes, you can import a video into a timeline and work with as video layer, performing basic corrections (cropping, adjustment layers, effects, etc. The number of available corrections can be increased by converting video layer to a smart object) - this iswill be applied to the entire video as a single object.It is also possible to split the video into separate frames and work with them as regular layers (this means that all Photoshop tools are available to you).After processing, you can export the video.
However, Photoshop is primarily a tool for editing individual photos (video frames).Working with video is much more convenient in After Effects or Premiere pro.
What do you mean by 'Clean up videos'? If you are asking about cropping out unwanted sections and rendering out to a new shorter video, then absolutely. You can also perform similar functions to those you might use on a still image.
Each video clip in the timeline will have its own group and layer in the Layers Panel. Right click that layer and make it a Smart Object.
You can then add an Adjustment layer above the video group layer, and it will affect every frame in the video clip.
Note that the Adjustment layer has a mask. You can use that to control what area is affected.
Cropping videos might be problematic, as the finished video that you render out has fit the format you are using. A 1080P video is 1920 pixels wide and 1080 pixels high, so cropping your video will reduce that. You can choose to render out to a different format, like 720P, ans scale the cropped video to fit. This approach works best if the original is 4K so you can crop and scale to render out to 1080P which will still look sharp on a TV screen.
Cleaning up video could mean to fix interference, and Photoshop can't do that. Apps like Handbreak (which is free) might make a difference, but in my experience, it won't perfectly clean up poor quality video.
Does this help? If you need more, then the more information you give us, the better the reply that you'll get.