No, don't be worried, a three year old should not be particularly concerned about school stuff. And, in accordance with my motto that children learn best through play, let your 3 yr old play, he's 3.
Looking up stuff on the internet will come soon enough. I don't think I would try to overly encourage your 3 yr old to sit with your 5 yr old. However, my dd, almost 3, enjoys playing some games (nickjr, noggin, starfall, etc. Disney kind of sucks, too slow) on the internet and if I get her started, she likes to look at google images of various animals, particularly sharks, frogs, and snakes. She can page back and forth on her own. Your ds may like something like that. My dd became interested in these things, games, because she watched her sister doing them and wanted to be just like her, so yes, they do follow the older sibs lead quite often in various ways.
In fact, younger dd has had to do exactly what older dd does for about the past 1.5yrs. It's been exasperating at times, but always fun.
It's only recently that that habit seems to be subsiding a bit. Her own personality is taking charge, kwim?
I would just encourage your 3 yr old in whatever he does take an interest in. As you know, every child is unique, follow his cues and try not to compare to your older ds. That's what I have to do. I suddenly realized that by this age, my older dd knew all her abc's by sight and had to quell the urge to start cramming abc's into my younger dd's brain,
We will just keep doing what we are doing.

In fact, younger dd has had to do exactly what older dd does for about the past 1.5yrs. It's been exasperating at times, but always fun.

I would just encourage your 3 yr old in whatever he does take an interest in. As you know, every child is unique, follow his cues and try not to compare to your older ds. That's what I have to do. I suddenly realized that by this age, my older dd knew all her abc's by sight and had to quell the urge to start cramming abc's into my younger dd's brain,

