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.
Open Photoshop
Go to Window on the top of the menu
Go to Default Workspace
The long narrow palette on the left is the Toolbox
That's where all the tools are :)
yes
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.
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.
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
Color Picker and Color panel. There are and non-destructive Adjustments to mix colors: Color Balance, Channel Mixer, Selective Color.
It is question for Photoshop and Illustrator developers, which tool is from which app but Illustrator have Photoshop raster filters, that's for sure.
Photoshop is a well known and popular artist tool for many people who create digital art or videos. The Photoshop Elements 8 allows for many features such as the recompose tool.