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.
Choose Ellipse tool from toolbox, hold down Shift key, click and drag.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
Photoshop is not bad, it is simply a tool.
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.
Quick Selection Tool creates selections by automaticaly detecting edges based on color and texture similarity of surounding pixels with clicked point. You can click or click and drag to create selection with Quick Selection Tool.
Photoshop is one such tool for that. Pixlr is another tool which can be used like Photoshop.
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 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.
There is no eyelash tool in Photoshop, but you can create a preset paintbrush so you'll only have to design them once.
The Move Tool allows you to rearrange layers in Photoshop by dragging and dropping.
Its the Zoom tool
I find the easiest way for me is to drag and drop. Open the folder your images are in and drag the images you want to import into the photoshop workspace and drop them. This will not delete, cut or alter the original images.You can either click and drag the image into the Photoshop window, or you can go to File>Open and choose the image you want to insert