Quickly flip the rulebook to look for appropriate entries
1) Can the Barbarian end rage “at will”, or is it a swift action as the description of rage dictates?
First, let's take a look at the Barbarian's rage power:
A barbarian can call upon inner reserves of strength and
ferocity, granting her additional combat prowess. [...] A barbarian can enter rage as a free action.
A barbarian can end her rage as a free action and is fatigued after
rage for a number of rounds equal to 2 times the number of rounds
spent in the rage. A barbarian cannot enter a new rage while fatigued
or exhausted but can otherwise enter rage multiple times during a
single encounter or combat. If a barbarian falls unconscious, her rage
immediately ends, placing her in peril of death.
And now, the Paralyzed condition:
A paralyzed character is frozen in place and unable to move or act. A paralyzed character has effective Dexterity and
Strength scores of 0 and is helpless, but can take purely mental
The tricky part here, "a purely mental" action isn't a defined system term. You can not use the argument "Entering/exiting rage is a free action, so it's neither a move or a standard action" since you can quick draw as a free action (and drawing is a move). So using only those two quotes, there is no explicit RAW.
But when you're focusing to give the better of yourself, it is a mental action. You have to think RAI on this one. The wording seems to be indicating that yes, a barbarian can end his/her rage while paralyzed.1
(And it's a free action, not a swift, as written in the question)
2) Can the Barbarian use Rage, which adds +2 to Will saves, to force another Will Save against the paralysis?
Raging however, does not grant an additionnal Will save, so unless you have another effect triggered by the Rage that explicitely allows you to retry a failed Will save, then you can't shake off the paralysis by raging.
1: Think of it as calming down. Admittedly, being paralyzed wouldn't make me (personnaly) feel calm, but it does nothing to prevent me from calming down either