It seems like your system was, or is, infected. I will definitely advise you to download MBAM, and run full system scan with it, to make sure that there is no malware remaining on the system. Due to the various amount of malware that are around, chances are that antimalware tools may find additional malware.
In the case of heavy infection, it's actually good to scan the system with different security software. Although Avast is quite good, but I would still recommend scanning with other security software, like MBAM, Superantispyware free, and Hitman Pro.
I will also suggest scanning with an antivirus removal CD, like Kaspersky Rescue Disc, or BitDefender Rescue CD. Both are available for free. You download the ISO images for the CDs, and write these images on a blank CD, and then boot the computer with those CDs, and run a scan. Very useful in the case of heavy malware infection. If you need the links, and cannot find them on your own, post back, and I will post the links.
It's important to make sure that there is no infection remaining on the system, otherwise, it's a chance that the infection will again increase with time. It's a pain yes, to scan the system with different security software, but if you system is infected, it has to be done. Some of the malware can be really hard to get rid of, and hide in places, or, just reappear.
Another thing, I would also advise to turn System Restore off, if you have it turned on, before scanning. Reason is, that malware often hide in System Restore, and then reappear again.
About scanning, well, you can scan as you like, like in a month, or more, or 15 days. Generally, if your system is clean, and you use safe browsing habits, and do not engage in risky activities on the internet, then there won't be any need to scan frequently, but if you do engage in risky habits, then depending on the activities, the frequency should be setup for a scan. It's easy to remember, just make a note of the date of the scans in a notepad or something to have a reference to.