Is Ash's time in Kanto's Safari Zone ever detailed?
Yes, it was shown in episode 35 of the original TV series. All he caught were Tauros', that's because whenever he tried to catch other Pokemon, a group of Tauros would just happen to run pass. That's why Ash only caught Tauros'. As of regards to Pikachu, it was held by Misty who wasn't participating. Kaiser ( in-charge of Safari ) also stated that the only rules were that they could only use Safari Balls and the Fishing Rod he gave them, and that they had to come back when they had ran out of 'Balls'. Break any of those rules, and his "Thunderbolt" would burn them ( this refers to the gun that he was holding ). There was no time limit and you could take your Pokemon in, but you can't use them to battle. Same with FireRed and LeafGreen, the Pokemon stays with you, but you can't use them in battle.
Hope this helps!