Paralysis does not deactivate a raised shield.
Your body is frozen in place. You have the flat-footed condition and can't act except to Recall Knowledge and use actions that require only the use of your mind (as determined by the GM). Your senses still function, but only in the areas you can perceive without moving your body, so you can't Seek while paralyzed.
You’re distracted or otherwise unable to focus your full attention on defense. You take a –2 circumstance penalty to AC. Some effects give you the flat-footed condition only to certain creatures or against certain attacks. Others—especially conditions—can make you universally flat-footed against everything. If a rule doesn’t specify that the condition applies only to certain circumstances, it applies to all of them; for example, many effects simply say “The target is flat-footed.”
Raise a Shield:
You position your shield to protect yourself. When you have Raised a Shield, you gain its listed circumstance bonus to AC. Your shield remains raised until the start of your next turn.
Paralysis is significantly less debilitating than it was in prior editions (where it was basically a death sentence). While you could make an argument based on the real-life use of a shield that paralysis would impede your use of a shield, the rules indicate that paralysis is not nearly as severe as one may expect: for AC, it's simply a -2 (which may match or beat the bonus from the raised shield). Neither paralysis nor flat-footed say that they negate a raised shield, so they don't.
The shield will no longer be treated as raised from the start of their next turn, even if they remain paralyzed. While it would presumably be in the same position (due to, y'know, paralysis), it could be flavored as enemies being able to maneuver around the now-static shield — while turns are consecutive in mechanics, they are concurrent in flavor, so while enemies would be acting against a raised shield while the character is paralyzed, in flavor it's all happening vaguely contemporaneously.
A paralyzed character cannot use Shield Block.
If the Fighter wanted to use Shield Block to reduce the damage, he wouldn't be able to do so after he has been paralyzed (..can't act)
This is correct, as you noted. The character can "use actions that require only the use of your mind (as determined by the GM)," but I doubt many GMs would rule that shield block solely requires your mind.
Inflicting paralysis depends on the source.
but if the Fighter had used Shield Block to reduce the incoming damage for the first attack to 0, would he still be deemed paralyzed, or does the condition require damage to be dealt (like Intimidating Strike)? Or does it dependent on the Monster / attack?
A ghoul, for example, does not need to deal damage to inflict paralysis: it simply needs to hit.
Paralysis (incapacitation, occult, necromancy) Any living, non-elf creature hit by a ghoul’s attack must succeed at a DC 15 Fortitude save or become paralyzed. [...]
I'm not sure offhand of any effects that require dealing damage to inflict paralysis, but they may exist. The ones I know of require hitting, not necessarily dealing damage: even if the hit deals no damage, it was still a hit, and the target will still be paralyzed (if they failed their save). While there is an exception, it's specific to persistent damage, and even that has a carve-out for GM adjudication:
Usually, if an effect negates the initial damage, it also negates the persistent damage, such as with a slashing weapon that also deals persistent bleed damage because it cut you. The GM might rule otherwise in some situations.