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.
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.
The Photoshop color replacement tool may not work as expected due to incorrect settings, overlapping colors, or limitations in the tool's algorithm.
In Photoshop, the flyout menu can be found by clicking and holding down on the icons in the toolbar. This action reveals additional tools or options related to that icon. For example, if you click and hold the Brush Tool icon, a flyout menu will display other related tools like the Pencil Tool and the Color Replacement Tool. Additionally, flyout menus can also appear in various panels, such as the Layers panel, where you can access more options by clicking on the small triangle or arrow in the panel's corner.