Are apps downloaded from Applanet safe for use?
Can they have any malware?
Applanet is that rather shady-looking place that claims to let users download and install 'thousands of free and paid apps' for free. Since the original authors of the apps have little say in whether their app appears on the site, I think it's fair to say that all bets are off when it comes to the apps' integrity.
Also bear in mind that it's recently been proved entirely possible to download malware from the official market (Google Blog entry).
So, in summary: