Pewter Gym
Brock, the first gym leader, in Pewter City is usually more difficult than he originally was in Pokemon Red or Blue. Pikachu is an Electric-type Pokemon, which means he is weak against the Rock and Ground Pokemon used by Brock. It is possible, but impractical to beat him solely using Pikachu. The Pokemon on Route 2 were changed in Pokemon Yellow, which is a great advantage for this fight. The male and female versions of Nidoran can be caught on Route 2. These are both Grass type Pokemon, which will do extra damage to Brock's Pokemon. Catch either one or both and raise it to level 10. It will easily win the gym fight against Brock.
Pikachu's Happiness
Pikachu is the only Pokemon in the game that has a Happiness stat. This stat needs to be at least 147 to get Bulbasaur from Melanie in Cerulean City. After you get Bulbasaur, the only noticeable effect of Happiness is how Pikachu reacts when you talk to him. This stat is raised if Pikachu gains levels. Using an item on Pikachu, even if it has no effect, also raises Happiness. Putting Pikachu into Bill's PC to remove him from your party or letting him be knocked out will lower Happiness. If you trade Pikachu to another Pokemon game and trade him back, his Happiness will drop to 0.
Raichu
One odd thing about Pokemon Yellow is that one of the uncatchable Pokemon in this version is Raichu, the evolved form of Pikachu. The starter Pikachu in the game will refuse to allow itself be evolved using a Thunderstone. It is possible to trade Pikachu to another Pokemon game, use a Thunderstone on it to make it evolve, and trade it back. This is highly discouraged. Any event triggered by Pikachu in Pokemon Yellow will not trigger if you evolve it into Raichu. Pikachu can be easily caught in any other version of Pokemon. It is better to catch one on another game and trade it to Pokemon Yellow. Only the starter Pikachu refuses to evolve. If you trade another Pikachu to the game, you can evolve it normally using a Thunderstone.