I couldn't tell you about the A4s. The Harrier had a combat manouver that conventional planes couldn't match, called Vector in Forward Flight (always called Viffing by the pilots) where they could scoot up, down and even sideways while in level flight. This made if difficult to get a missile lock on them, and almost impossible for guns. They could also, of course, fly backwards. To give the Argentines their due, they were skilled and brave pilots just doing their jobs, but had to come in fast at low altitude and either let go their French Exocet sea-skimming anti-ship missiles, or bombs, then high-tail it out with strict instructions not to engage in dogfighting. They lost several more to Brit. army land-based SAMs.
The Harriers (actually, mostly the Sea Harrier version) flew defensive patrols and got radar warning from the picket ships, enabling them to be in the right position to let go their (American) air-to-air missiles.
There was no defense against the Exocet. Once you saw it on radar you had at most 30 seconds before it hit, and with the image clutter in San Carlos bay mostly they remained unseen until too close, and when the missile was seen visually, you had about 6 seconds to kiss your ass goodby. The ships had chaff dispensers that could have protected them, but these were designed for the open sea where you had plenty of radar warning. The French had technicians helping the Argies to perfect the Exocet while the battle was going on, just one more reason for the 1000-year-old antipathy between the Brits and the Frogs.
A lot of stuff happened in this conflict that had not been forseen. The British destroyers and frigates had an effective radar-controlled antiaircraft missile system. It would lock onto an incoming plane and after that there was no escape for it. Unfortunately, the designers had not considered what would happen if two planes came in abreast. The radar hunted between one and the other, then as the software had no imagination and couldn't decide which to lock on to, it simply shut down. Several ships were lost that way. That's what happens when non-flyers design such things.
For the Argies, they had problems with their bombs going straight through the superstructure of some of the ships without exploding, or rather exploding in the sea afterwards. The fusing delay in milliseconds had been designed for steel targets, but the British destroyers and frigates had alumim(i)um superstructures. Unfortunately, one or two embedded correspondents, keen to get a scoop, radio'd this back to their newspapers, with the result that a couple of the tabloids had headlines like STUPID ARGIES DON'T KNOW HOW TO FUSE THEIR BOMBS and then the details. From that point on, the Argies reset their fuse delays and several more ships and a couple of hundred sailors, marines and soldiers were lost. Makes you want to strangle someone.
I may have told you that Mark, my wife's nephew, was a crewman on the QEII. This ship was very quickly (a matter of days) commandeered and converted to carry helicopters by fixing steel plates to the decks. The regular crews were told that they didn't have to sail on what may have been a one-way trip (it was, of course, the Argentines' # 1 target and would, apart from the loss of life, have been a tremendous propaganda victory for them, and demoralizing loss to Britain). However, Mark said he wouldn't miss it for anything, and has since told us several stories of Prince Andrew (third in line to the throne, and known as "Randy Andy" because of his reputed c*cksmanship) operating as a helicopter pilot from the ship.
(Although I'm anti-royalty by philosophy, I have to admit that they have never evaded front-line service. Prince Michael, also 3rd in line at that time, was killed serving in the RAF in WWII, and several other nobles served (e.g. Lord Lovatt who led the Royal Marine Commandos at D-Day), and some were killed. And the King, Queen and two princesses never left London during WWII, even in the height of the Blitz. Buckingham Palace was hit twice, one time blowing the windows in on them at dinner. The King said "now I can look the people of the East End in the face.")
The whole war was, of course, stupid. The Falklands, which were very important strategically in both World Wars, from 1945 were just inhabited by a few score people, mostly sheep farmers. An Argentine writer characterised the war as "two bald men fighting over a hairbrush." However, it was British sovereign land. You have to make a stand somewhere.