Correct, keeps you from escaping every forward slash (First virtue of a programmer: lazyness).
Almost. '.+' means any character, one or more times, with greedy matching. Meaning "as much as possible", so for most strings you can leave the caret out.
\w means any word character (alphanumeric + '_'), which is matched one or more times with non-greedy matching (aka 'as few as possible'), so it matches only up to the next forward slash. Repeat for the part after the slash.
Correct

$1 holds the contents of the first capturing group from the last regular expression. Anything between '(' and the matching ')' is a capturing group (can be nested, too). Example:

Code:

$var = "Hello World";
$var =~ /(\w+) (\w+)/;

$1 would be "Hello", and $2 would be "World" (sans the quotes).

Best bet would be chomp. It's possible to match the newline inside the regex using the 'm' and 's' switches, but my personal preference is chomp, as it's intent is more clear.