Color Picker and Color panel. There are and non-destructive Adjustments to mix colors: Color Balance, Channel Mixer, Selective Color.
Color Replacement Tool you can use to replace existing colors on image with Foreground color by painting with brush.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
You can use the pen tool, quick selection tool and lasso.
You would use the marker/pen/brush tool, or the paint bucket tool.
Photoshop Lightroom does not have such a tool. Anyway you can use external editing software like Photoshop or Photoshop Elements. See related links for more details.
Use the croping tool.
It is question for Photoshop and Illustrator developers, which tool is from which app but Illustrator have Photoshop raster filters, that's for sure.
Adobe Photoshop
There isn't drag tool in any Photoshop version. To move things around you can use Move Tool or Path and Direct Selection tools to move paths and shapes.
Select Smudge Tool in Toolbox and paint over areas on image
The erase tool in Photoshop will allow a person to remove parts of a photo. Also using the select tool and then clicking Delete will remove part of the photo.
For selections you can your the Marquee Tool, Lasso Tool, or Magic Wand Tool. To cut that selection you can use the Move Tool, or the Ctr-X keyboard shortcut.