Is there a way to get my Golbat to like me quickly, such as the groomer from GSC?
Yes. Walking 245 steps will increase its Happiness Rating by 1 point. Leveling up a Poke increases its HR by 5 when its HR is 0-99, 3 when it is 100-199, and 2 above that. Feeding it vitamins will increase its HR by 5 when its HR is 0-99, 3 when 100-199, and 2 above that. Also, winning important battles (i.e. gym battles, Weak5) increase its HR by 3 when its HR is 0-99, 2 when 100-199, and 1 above that. Also, when you beat the Weak5, you can go visit Gary's sister and she will groom your lead Poke and then tell you generally how happy it is. Having the Poke hold the Soothe Bell (found in the Pokemon Tower - use the Itemfinder where Mr. Fuji was standing).
There are some myths about things that affect a Poke's HR that just aren't true. They are putting a Poke into the PC, letting the HP fall into the red, or walking around with a status effect (i.e. SLP, PSN, etc.). You also cannot increase HR by healing a Poke, giving it an item to hold (not called Soothe Bell), or battling wild Pokes.
Just remember that every time you trade your Poke, its HR is dropped (or raised) to 70. So make sure you don't time on Eevee, raising its HR in FRLG and then trade it to RSE, expecting it to evolve because it won't. All the HR points you put into it will be lost. Trade to RSE first, raise its HR and THEN evolve it.
What pokemon should I battle to get effort points in defense for my pikachu?
NEVER put Def EV points on Pikachu. It is a complete waste since its base Def is so low that the EV points won't even help. You should instead focus its EV training on SAtk and Spd. The best place to train for SAtk is in the Pokemon Tower, on 7F. There you will encounter Gastly (1 SAtk) 75% of the time and Haunter (2 SAtk) 15% of the time. Cubone is here 10% of the time, but you can just flee. For Spd, Route 1 is a great spot early on as you will only encounter Pidgey and Rattata, both of which give you 1 point. Diglett's Cave is another great spot since the levels are higher and you also encounter Dugtrio 5% for 2 Spd EVs.
The best place to train for Def EVs is on Route 21, which is south of Pallet Town. You will only encounter Tangela there. Early in the game, you can battle Metapod (10%) and Kakuna (5%) in Viridian Forest for 2 Def EVs, or if you want encounters more often you can battle Geodude (35%) and Onix (5%) at Rock Tunnel.
Seriously though, don't waste Def EVs on Pikachu.