New to Beijing - several questions

Hi,

I arrived to Beijing at the beginning of March, currently working in our Beijing office and have a few questions:

1. I got a China Mobile SIM card at the airport, but soon discovered that in my phone it works only as 2G (no 3G or 4G), because the 3G network of China Mobile uses a different technology. Anyway, it seems now that I have almost no money on the SIM card left, so I might either recharge it or buy a card of another operator.
It would seem that China Unicom has a 3G network compatible with international standards (i.e. WCDMA), but where can I get one? In Asian countries usually they sell SIM cards at every corner, but here in Beijing (or at least in Wangjing) where I'm staying it's difficult to find such places. I've been to a few malls, but didn't see shops selling SIM cards.

2. Taxis: seems not to be always so easy to catch one. The other day I had to walk back from the office to my apartment (5km!) because no taxi would stop in half an hour. Even taxis with no customer often are unwilling to take people. Following the suggestion of a colleague I installed a dididache app, but am not sure how that works.

3. The overall pricing level seems to be a bit high for a low cost location, but then I guess that Beijing is not a low cost location, right? Prices for some things are even higher in Beijing than they are in Germany.

4. I've been trying to buy a good, big kitchen knife with which to cut vegetables (I cook for myself). In Munich these are easily available everywhere, but not so in Beijing. Went to some shopping malls and IKEA, but could not find it. Are perhaps people afraid to sell these or are these considered "dangerous weapons"?

5. Chinese classes: how can I find a teacher (I have some basic Chinese skills already). Is the classifieds section of TheBeijinger the place where to find a teacher? How much do classes cost?