The transform tool allows you to take an image and stretch it any way you want without it pixelating. ie. bigger, smaller, warped...
If you hold down shift while you do this it will keep its original proportions and wont warp.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
To crop one layer in Photoshop for the desired composition, select the layer you want to crop, then use the crop tool to adjust the size and position of the layer within the canvas. You can also use the transform tool to further refine the cropping.
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.
First click on layer with pixels you want to warp (layer can not be background layer, must be regular layer), in Photoshop CS5 and newer go to Edit > Puppet Warp or Edit > Transform > Warp.
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.
ctrl-t is free transform.
I assume you mean "Photoshop CS3" rather than Playstation 3. Press "B".