#1 - I haven't heard much about real estate fraud happening here, but I suppose it is possible. The best thing to do is be here yourself, with a local lawyer who should have already investigated the property and the people selling it (all easily done through the Registro). There are problems with squatters, when foreigners buy property but never actually come down to Costa Rica nor have anyone in charge of taking care of it. However if you intend to move down and live in the place, this shouldn't be an issue.
#2 - Really does depend what area you live in. The apartment I'm in right now for another few days, costs $300/month. It's in a pretty nice area, university area, with lots of businesses and nightlife. It's 2 bedroom apartment (so has living room, kitchen, laundry room, bathroom and 2 bedrooms).
If you go for more expensive, "foreigner" areas like Escazu, I think you can pay $700-1500 for the same thing.
Buying a house is recommended right now, as property value here is rising steadily. I just bought mine at $120K in a developing region 5 mins from where I live now, and it's already worth $150K (appraised by three different banks). You get a lot more size/rooms for your money too than you would anywhere in the US/Canada.
#3 - It's available almost everywhere now. You have options from cable to isdn to adsl. You're looking at about $35 for 128 or 256K speeds, $70 for 512K , and newly offered is ADSL of 1-4 megs ($100-300) a month.
Hope those answers help
