As a Microsoft Certified Professional, I will say that this does sound suspicious.
Microsoft Office is about £80 for a key for the basic version. If it is genuine, there will be a sticker on the computer or given to you. On a laptop, it's probably underneath. Likewise, if your Windows is genuine, there will be a Windows sticker WITH a key on it - there are some laptops that are for educational use that don't actually have a key on the sticker. Whilst they are legitimate, they are often formatted and illegal software is installed.
No software should have its updates disabled - telling you do do this is a clear sign of piracy.
If you must have WinRAR, you will find that you can get a 'free' version legitimately through TrialPay:
http://www.trialpay.com/checkout/?c=2d3e25c&tid=A7DDnllThis is completely legitimate, but you will have to sign up to another service to get it. This could be something such as signing up for a Flash game site and buying a £5 game, or a casino site and depositing money.
Personally, I would stick with free software and go for 7-Zip. It's great software!
http://www.7-zip.org/As for the Microsoft software, you could run the Genuine Advantage tool to see if your Windows and Office are genuine. Unfortunately, this may disable or restrict your software if it turns out to be pirated. You can find more information here:
http://www.microsoft.com/genuine/Microsoft used to operate a "grass and get a genuine copy" policy if you told them about someone who sold you a pirated copy of their software, but I don't think they do any more. Personally, I would still report the company and take action against them, as they have missold you a product. Here's Microsoft's report piracy link:
https://www.microsoft.com/en-gb/howtotell/cfr/report.aspxIncidentally, you have two free alternatives to Microsoft Office.
Firstly, you could download openoffice.org from
http://www.openoffice.org.
Secondly, you could use Google documents. If you have a Gmail account (or a Youtube account), sign in and you should find a link at the top to documents. On that page, you can create new documents. The advantage of this system is that it works in your browser. This means that there's nothing to download, what you type is saved the second you type it, and you can access your documents from anywhere.
Sorry to be the bearer of potentially bad news, but hopefully this should have given you some idea of how to resolve the issue, and some free alternatives!