|It may not be AutoComplete entries, but search "suggestions". AutoComplete gives a list based on search queries a person typed into that text box before. Search Suggestions are provided by search engines based on what they think you may be searching for.|
You mentioned that the suggestions (either autocomplete or from a search engine) are offensive. I know there have been times that Google's search suggestion algorithm has been less than perfect and the suggestion could have been seen as offensive (depending on the person) or even pornographic, but they continue to adjust and improve it. One thing you could do is disable Search Suggestions.
Right next to the search bar in the upper right is a magnifying glass and a downward arrow. Click that arrow then click Manage Search Providers. A window will popup. From there, you can see the search engines installed to your web browser's quick search toolbar. Right-click a search engine and select Disable Suggestions.
Buying a used computer is alright, but you should (or the technician you bought it from) format the hard disk drive and reinstall the operating system (don't forget system drivers) shortly after. 1.) The previous owner may have data that isn't your business to view. 2.) The computer may be infected with malware and reinstalling the operating system typically cleans it up. 3.) Any unnecessary programs the previous owner installed are gone and you get that used disk space back. 4.) Any other software problems will be gone. The process of reinstallation can be tedious to a non-tech-savvy person, but I think you'll benefit overall afterward.
Lastly, if you're not satisfied with Internet Explorer, you could try an alternate web browser like Mozilla Firefox, Google Chrome, Opera, or Apple's Safari.
Apologies if I don't respond to your reply immediately. I don't check this site daily, but you're welcome to PM me as a reminder.