With Move tool you can Move objects (layers) in your document, or move layer from one document to another. Also when this tool isactive you can align and distribute objects from Options Bar (below menus)
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.
In Photoshop, the pucker tool is part of the Liquify tool. The pucker tool is used to move pixels towards the center of the brush area.
A tool that lets you move your image or selected parts of it around on your canvas.
The Move Tool allows you to rearrange layers in Photoshop by dragging and dropping.
Tools are essential to work in Photoshop, there are Move tool to move objects, Type tool to type text, magic wand to create selections, zoom tool to zoom image in and out and many, many more.
All tools like Move tool, Brush tool, Type tool live in Toolbox or tool panel as you say. It is one of most important panels in Photoshop, you can not access tools in Photoshop from any other panel in Photoshop.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
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.
Photoshop is not bad, it is simply a tool.
Alt key or Option on Mac.
Photoshop is one such tool for that. Pixlr is another tool which can be used like Photoshop.
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.