I would check with your bank about what kind of safeguards they have for you on your debit card. If not, it's always good to have a credit card with a nice low limit for internet stuff. Almost all credit cards allow you to do what's called a "chargeback" where you can cancel any fraudulent charges if you report it within a few days. But, and I can't stress this enough, check with your specific bank or credit card issuer about their policies. If you don't understand the fine print, give them a call on the phone and make them explain it to you. Another good idea is to set up spending alerts with your bank. When my debit is used for a purchase of $200 or more I get an email (or SMS) within an hour from my bank letting me know.
As for purchasing apps on the market I think it's reasonably safe since it's mostly handled by Google Checkout. However nothing is guaranteed, especially on the internet. Google checkout is probably about as safe as Pay Pal, which is reasonably good but not perfect.
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