There's quite a few questions, and a few misconceptions in this post. To start with, Coventry was deployed off Pebble Island to act as a SAM trap and radar picket. These roles require a ship (or ships) to be deployed along the threat axis (the direction the hostile aircraft are coming from). In this position, she can provide early warning of air raids to the main body. If, as Coventry was, she is armed with SAMs, then she provides the attacking aircraft with a tactical dilemma - do they expose themselves to fire from the SAM trap, or do they pass up the chance to attack the main body to deal with the SAM trap. While this does pose some risk to the ship, she's much more expendable than the carriers or transports in the main body. Coventry was not alone in the SAM trap role on the 25th May - she was accompanied by the Type 22 frigate Broadsword, in what was called a Type 64 pairing, from the type numbers of the two ships. The Type 22 was armed with the Sea Wolf SAM, a short-range SAM designed primarily to destroy missiles. This pairing, in theory, was well protected against all threats. Coventry's Sea Dart allowed it to dominate the airspace at high altitudes and long ranges, while Broadsword's Sea Wolf provided protection against threats at lower altitudes and closer ranges. Two aircraft were shot down by Coventry on the 25th, one causing a raid to turn back. Both ships were also armed with guns to provide close in defence - Coventry had its 4.5in and two 20mm cannons, while Broadsword had two 40mm and two 20mm, with both ships being unofficially armed with machine guns as well. However, of these, only the 4.5in was radar directed.

Unfortunately, this theory was somewhat flawed for the fighting in the Falklands. The RN had designed its ships and weapons for the war it expected to be fighting against the Soviets. The Soviet threat mainly consisted of large, high-flying supersonic missiles and bombers. As such, Sea Dart and Sea Wolf were designed to be much more capable against these threats. The Argentinian aircraft made their attacks at low level, and used terrain well, making it hard for British radars to distinguish them as targets - while the British could have designed radars that were more capable in such circumstances, this was felt to be unnecessary for much of the time. Additionally, Sea Wolf was a new system, having entered service three years earlier. There were still bugs in its computer system, partly stemming from expectations about use cases for it. It was designed to target one or two targets, and the multiple targets provided by the Argentinian attack caused it to shut down. Once this had been sorted, the other flaw of the Type 64 became clear. Coventry's manoeuvring blocked Broadsword's line of fire, preventing Broadsword engaging. It was difficult for both ships to manoeuvre independently, while allowing both ships to engage fully.

As to why Coventry didn't have CIWS, the technology was relatively new, it was still buggy, and the RN was unconvinced that it was worth the money. The losses suffered by the RN were a major justification for the acquisition of CIWS - and led to the Type 42s being refitted with Phalanx soon after the war. The anti-missile missiles in the RN were provided by the Type 22s, as the Type 42s were always expected to be operating in combination with them. However, later upgrade to Sea Dart and the Type 42's radar outfit allowed it to better engage missiles and low-flying targets (in the Gulf War, Gloucester would be able to shoot down an Iraqi Silkworm SSM with Sea Dart).

This sort of low-level attack against a SAM armed target was in no way unique. The Argentinians made multiple attacks of this sort against British ships during the Falklands war, especially in the confined waters of San Carlos. For example, on the 21st, the RN lost Ardent to just such an attack, while Argonaut and Antrim were damaged. On the 23rd, HMS Antelope was lost. These attacks weren't limited to the Argentinians either. The RN and RAF had been training for similar attacks with the Blackburn Buccaneer since it entered service in the early 1960s, while the USN had the A-6 Intruder and A-7 Corsair for similar roles. Low level attacks have always been a default for air attacks against SAM armed targets, or even just those with radar-directed guns.

The Argentinians did have a good idea of the capabilities of the Type 42 - the Argentinian Navy operated two, as the Hercules class. This meant that they had a good idea of the abilities of Sea Dart, and the Type 965 radar. There is some evidence that this instructed their choice of attack patterns, but as noted above, this is a standard tactic for use against targets protected by SAM. As to why they didn't use Exocet against Coventry, its because they had very few of the air-launched versions. The sea-launched version was out, as the Argentinian Navy didn't want to risk its surface units inside the Exclusion Zone due to the threat of British subs, exemplified by the loss of the General Belgrano. The Argentinians had only five of the air-launched version, and considered that these were far more useful for targeting the Task Force, with its carriers and transports, than for targeting the outlying pickets.

At the time of her sinking, Coventry had been paired up with the Type 22 frigate HMS Broadsword which was equipped with point air defence in the form of Sea Wolf missiles. The intention initially was to draw air attacks away from the carriers (HMSs Invincible and Hermes), but extended to acting as a decoy for elements of the Task Force operating in San Carlos bay. This tactic was adopted after the loss of HMS Sheffield, Coventry's sister ship, which had reduced the Task Force's air defence capability.

To do this Coventry and Broadsword had to adopt a position sufficiently close to San Carlos to be an effective decoy and this put them close to land, but not necessarily at a great disadvantage. During the fateful attack, Coventry's radar struggled to pick up the first wave of Skyhawks and Broadsword's air defence system suffered a malfunction. Coventry repositioned herself to reduce the threat from the second wave, but in doing so put herself in Broadsword's line of fire so although Broadsword had sorted out her air defence system, she couldn't open fire. The loss of Coventry was more a matter of unfortunate circumstance than tactical incompetence.

The Argentinians understood the Type 42s very well as they operated two of their own (ARAs Hercules and Santisima Trinidad) and the 42s were prime targets as they had to be eliminated to make an attack on the British carriers possible. Their use of terrain masking against Coventry shows a good level of understanding of her weaknesses, but is also a classic attack profile against any radar-equipped surface target. The attacks also show little appreciation of the Type 22's capabilities and so I would suggest the Argentinians didn't have a full understanding of the situation.

The decision to use ships as decoys for air attacks was very risky and of the five Type 42s deployed to the Falklands, three were hit in air attacks with two lost. The 42s were designed as medium to long range air defence and the Falklands experience led to improvements being made to the class to improve point air defence and missile defence.

The Argentinians did use air-launched Exocet missiles against British ships, notably sinking HMS Sheffield and MV Atlantic Conveyor and damaging HMS Glamorgan. I don't have any direct information on how many air-launched Exocets the Argentinians had, but British actions to disrupt Argentinian purchasing and Argentinian attempts to adapt air-launched missiles to surface launchers suggest they didn't have very many which would explain why they weren't used more often. There is also the possibility that they were reserving Exocets for use on higher-value targets such as the carriers.