1) Does the text on WEAPONS resolve just for playing the weapon on your turn or do you have to have the required ammo for that weapon first BEFORE using the text on the card?
So for example the text on the rifle states you pick a player to discard a card from their hand. Does this happen only if you have ammo for the rifle or it can be used just for having the rifle in hand (and play)?
You need to play the weapon AND have enough ammo to fuel it in order to get the benefit.
2) Since the various actions can be performed in any order, are the two examples correct for one turn (assuming all relevant cards in play):
a) Play a hand with two weapons. Have only enough ammo for one. Explore and use the weapon with ammo. Then play an action card (example: Item management) and upgrade one of the 0 cost ammo to the 30 cost ammo.
b) Play a hand with a grenade and weapon with ammo. Explore and use weapon and grenade to defeat an infected. Trash grenade. Do a buy phase and buy back grenade.
If you only have ammo for one weapon, why would you play both?
Item Management can't be used on ammo you played (to use your weapons), only unspent ammo not used and also it "gains" the next expensive ammo, meaning that new ammo goes to your discard pile.
Example B) is right. You can also combo the order with buying say Shotgun, then using Reload to take it from the discard pile.
3) Does cards like Police Station and A Gift? force a reshuffle of the discard pile if you run out of cards in your inventory trying to fulfill the text requirements (draw and discard until weapon found and +2 cards respectively)?
I'd say yes.
4) Spec Ops rifle special is to force all players who have not explored that turn to discard a card from hand. What exactly is a "turn"? Does this special apply to all players until my turn come around again? so if they don't explore they lose a card)
This weapon is from the Nightmare expansion which I don't have and couldn't find an image of it on BGG, so can't help without the full text.