If you read the whole wiki, it’s pretty clear that the use of chess engines was not prohibited, and a team of engine users was suggesting moves. The World team also tried unsuccessfully to simplify to a position where tablebases could point out perfect play. It should be pretty clear that the analysis offered by the World team leaned heavily on external help, in this case engines and tablebases.

With all due respect to Barcot, Felecan, Krush, and Paehtz, it would’ve been highly unlikely that without the aid of engines, they would’ve had a close game against Kasparov. Barcot is easily the most accomplished out of these players, and by 2001 (the earliest available data) he was still “only” a 2600 player. In 1999, Kasparov was still a 2800 player at the peak of his powers. None of those 4 players would’ve stood a chance against Deep Junior, an engine used by both sides.

Had Kasparov gone out and purchased the best computer hardware at the time, and had it run analysis 24/7, would that have been cheating?

The article alludes to the fact that in 1996 Karpov crushed another World Team. I would argue that the development of competent chess engines during the period between the two matches is a key reason why the World team fared much better the second time.

Chess is a game of perfect information. Here, what Garry did can be best characterized as a “shortcut”. If he had run an engine 24/7, it would’ve produced moves better than what the World team played.

I've mixed feelings. At first I lost some respect for him when he said he cheated but then I realized he conceded that he cheated and that is also respectful.

I mean honestly, when it is not against the rules it is just good meta-gaming. At least when playing on this level. And the game was still very interesting!

Is it “reading their thoughts” if they’re openly communicating them? Would you consider it cheating if someone wrote down their ideas on paper during a game and didn’t stop you from reading the paper?

A lot of sports have a rule about unsportly behaviour where others rules don't specifically cover the infinite variety of ways a person can be morally obstructing the spirit of the game. I would definitely say reading your opponents strategies fall under that.