Tool which allows you to crop part of image. Activate Crop Tool then click and drag to draw shape. Shape will be surrounded with dotted line, then press Enter on keyboard to keep that portion of image, rest of image will be cropped (deleted).
A good way to explain the crop tool in Photoshop is to imagine you have a printed-out photo that is a little too big for the picture frame you want to put it in. Many times we get out our scissors or a trimming knife and cut it down smaller so it will fit. This is what the crop tool does.
When you choose it, the next step is to draw a box around the area you want to keep. You can keep re-drawing, or you can use your keyboard arrow keys to nudge the box so the subject is nicely centered. Once you're happy with the composition, click Enter or Return and Photoshop will cut away everything outside of your box.
Other reasons to crop, by the way, are to improve your composition or to change its proportions (for example from a rectangle to square shape).
You must slice image or to create slice from layer. Slice tool is grouped with Crop tool in toolbox.
You can do that with Crop tool or from Image -> Image Size. See ralated link for good explanation how to do that properly.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
In the bar on the left hand side of the screen, choose the thing that looks like a square with a cross through it. [near the top] Once you have chosen that, drag the mouse over the area you want cropped. The part that will be cut off should appear in gray. Right click and choose "Crop", or "cancel" if you want to cancel your selection.
Photoshop is not bad, it is simply a tool.
Using Crop tool you can crop image and increase resolution. Activate Crop Tool then type dimensions and resolution in tools options bar (just below menus) in Width, Height and Resolution fields then drag over image with Crop Tool to select area and confirm on check mark in tools options bar or by pressing Enter/Return. In Photoshop CS6 after activating Crop Tool click on Unconstrained on the right side of Crop Tool icon in tools options bar and choose Size and Resolution. In Crop Image Size & Resolution dialog type dimensions and Resolution or just type Resolution, confirm on OK then use Crop Tool. Visit related links for more details with similar topic.
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.
Crop, top, hop.
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.