I have just syarted playing four days ago, and although I am having fun, I don´t seem to progress in the game.Although I have managed to solve puzzles 4 and 5 I can´t solve puzzle 3. Island events seem very few, is this normal?

A lot of the puzzles need certain conditions to be able to be solved. I am not 100% sure which one is 3, but if it is what I think, you just need to continue building up a strong healthy village (this includes making sure they have plenty of food), and the puzzles will slowly start coming together

As for Island events, I don't think there is any way to predict what or when you will get them, so I wont be too worried that you haven't seen many yet

Savi

no what really works if u get a choce is to click like drink it and if somthing bad happens restart ur pda and it wont save it

Puzzle 3 is related to building I think.

I didn't know where this question should go. Be that as it may, my Golden Child was born. I got all the women pregnant...or so I thought. At closer look, there is a striking woman with platinum hair who was never pregnant. The Golden Child was not cared for by any of the other women;their offspring are all accounted for. Is this a coincidence, or is this woman supposed to be the "mother" of the Golden Child?
Gail

The Golden Child's birth does not occur in the same manner as that of normal children. The child can be born to any woman in the village, however there is no period of nursing. This child skips the baby stage so the mother is never carrying him or her around.

So I've had full research for a couple of days, and many children born, but no GC. Is it just a matter of patience? (Not my strong suit.)

Yes, it's just a matter of patience if you have fully researched all village tech and completed the prerequisite puzzles. The birth usually happens within a fairly short time, but one person reported having waited 41 days for puzzles 10 and 11 to unfold! That's something that's being looked at for the v1.1 update.

So I have only 9 of 12 puzzles solved (the first nine). Does that mean I'm waiting in vain? Are there other things I need to solve before GC shows up?

No, you're not waiting in vain. Once you're at that point in the game, you just need to be patient and make more baby villagers as space allows!