Are there keyboard shortcuts to move paragraphs up or down while editing text

Here's how you can get ⌃ Control+arrow keys to work like you describe. Copy the following property list into ~/Library/KeyBindings/DefaultKeyBinding.dict (you can create the directory if it doesn't already exist):

{
    "^\UF703" = ("moveWordForward:", "moveWordForward:", "moveWordBackward:");
    "^$\UF703" = ("moveWordForwardAndModifySelection:", "moveWordForwardAndModifySelection:", "moveWordBackwardAndModifySelection:");
}

This will set up ⌃ Control+arrow to navigate to the beginning of the next word (by using OS X's normal navigation three times: to the end of the current word, end of the next word, then back to the beginning of the next word). I also included a version that works with ⇧ Shift so you can select text as you go.

Caveat: this will only work in Cocoa apps, but I think the normal ⌥ Option+arrow navigation does too. Also, make sure to relaunch your apps!

According to this blog post, you can create a file called ~/Library/KeyBindings/DefaultKeyBinding.Dict (you might have to create the KeyBindings folder in your Library folder).

In that file, you need the following content:

{
   "@\UF702"  = "moveWordBackward:";
   "@\UF703"  = "moveWordForward:";    
}

(see the linked blog post for other Windows features you might want to recreate)

Not all programs that use text fields will use the default keybindings, but this will help with many programs.