Is there a way I can move the mouse pointer using the keyboard?
In System Preferences, choose Accessibility > Mouse & Trackpad (or search for “mouse keys”). Enabling Mouse Keys (which can usually be done by tapping Option five times) allows the numeric keypad to function as an 8-direction “joystick” (7 = left+up, 8 = up, 9 = right+up, etc.). Use the keypad's 5 to click the mouse (press it twice, quickly to double click; hold Control while pressing to right-click).
Yes. Let's assume you're in a document editor and you have a bunch of text you'd like to navigate. You can use the arrow keys ← ↑ → ↓ to move one character in either direction horizontally, or one line in either direction vertically.
To move to the beginning or end of a line, type ⌘← or ⌘→, respectively. ⌘↑ and ⌘↓ move to the beginning and end of the document. In areas where these shortcuts don't work, such as in the Terminal, use ⌃A and ⌃E instead (which can be used in most Cocoa text controls).
You can move one word left or right by using ⌥← or ⌥→, respectively. Likewise, ⌥↑ and ⌥↓ move to the beginning and end of a paragraph.
As Chris Johnsen points out in the comments, you can also use "other Emacs-like bindings (⌃F: →, ⌃B: ←, ⌃N: ↓, ⌃P: ↑, ⌃T: transpose (swap) characters)". Chris also mentions some interesting subtleties with soft-wrapped text, where "⌃A and ⌃E work on the whole line while ⌘← and ⌘→ work on the current portion of the display-wrapped line". Thanks For that.
Not sure if this is what your vague question was referring to, but you can definitely move the cursor using the keyboard almost anywhere in Mac OS X.