Kids differ enormously in how quickly they acquire languages. My own son, brought up bilingually, didn't say more than six words in any language until he was three, though he clearly understood both English and Italian. But by three months later he'd zoomed through the stages that take most kids 18 months and was speaking Italian like a normal 3 yr old. But English didn't come until much much later and at first there was a lot of interference. Now, at nearly sixteen and having attended both English and Italian schools, he's completely (and enviably) bilingual.
That doesn't mean all bilingual kids will be late speakers. Many kids don't have the early problems that he had sorting them out, and yes, three languages are feasible. I know a number of kids with parents of two different nationalities living in the country of neither who cope with three.
Can they learn them all by three years of age? Depends what you mean. I'm sure that if they've been brought up from birth with equal exposure to all three, they'll understand them. Which they speak will depends, as I said before, largely on the needs of the situation. My son didn't speak to me in English because he knew I understood Italian and if his Dad could speak to me in Italian why not him too? Nothing bolshy about it - to a kid it's just common sense. They don't see any "value" in knowing different languages - just in communicating.
Obviously, I'm very pro bringing kids up multilingually. But I do think people have very unrealistic expectations about how "easy" they'll find it. Kids have to be exposed to language for hours and hours and hours in order to acquire it - calculate how many hours of talk a monolingual three year old has heard, and how little of that language s/he actually understands and can use yet. Say they're awake 12 hours a day - it's over 13,000 hours. Not to mention that the child needs to use that language to get the things s/he wants.
And then along come some monolingual parents, decide to send their child to you for 2 hours a week, and thirty weeks later are annoyed that the child isn't fluent in English. LOL.
If you're interested, this is
a list of some books on bringing kids up bi- or multilingually.
As for websites - Yes. If you look at the bottom of people's messages you'll see links to their websites if they have them. My two ELT sites are listed below. Hope to see you there!