Can I download Windows XP and save it to a disc ?

NO, you can't do what you are planning to do.

The files available to download called "Windows XP Service Pack 3" are updates to a complete installation of Windows XP.  You may either download an ISO file (or "image") -- which is what your link is -- or an executable file (http://www.microsoft.com/download/en/details.aspx?id=24).

The ISO or image file is used to create a CD by using software capable of doing that, such as (free) ImgBurn.

In either case, what you are getting is the "service pack" and not the complete Windows operating system.

You need a Windows XP installation CD.  These may be "gold" (as initially released) or you may find one that incorporates service pack 1 or service pack 2 or service pack 3.  If you obtain a pre-sp3 install CD, you'll have to update the installation promptly after installing.  You can go from sp 1 directly to sp3 without needing to install sp2, but if you get a "gold" install CD you must first install sp 1 or sp2 before installing sp3.

Because Microsoft stopped selling Windows XP some time ago, genuine installation CDs are getting more difficult to find. 

Although the rep from your computer's manufacturer was correct that you could buy any Windows XP installation CD and install it, the manufacturer was obligated by its license from Microsoft to provide you some method of re-installing Windows when you purchased the computer.  This may have been a hidden restore partition on your hard drive or some CD/DVD supplied with your computer.  I assume that you have lost or damaged whatever was first supplied and the manufacturer is no longer able or willing to replace it with a CD.

Here are some tips from long-time MS MVP PA Bear:

HOW TO get WinXP SP1 or SP2 fully patched after a "clean install":http://groups.google.com/group/microsoft.public.windowsxp.general/msg/a066ae41add7dd2b

1.  Download & save the installer for WinXP SP3 to your desktop:

http://www.microsoft.com/downloads/details.aspx?FamilyID=5b33b5a8-5e7...

[Yes, you can skip SP2 if you're running WinXP SP1.]

2. Read & heed:

http://msmvps.com/blogs/harrywaldron/archive/2008/05/08/windows-xp-sp...

3. Logged in as Administrator, if necessary, double-click on the saved file to install WinXP SP3.  Follow all prompts; be patient, and reboot twice when the install completes.
4. Do Resolution Method 2 here (trust me):

http://support.microsoft.com/kb/943144

5. Go to http://windowsupdate.microsoft.com | Install any required software then click on CONTINUE | Select CUSTOM and scan | Install any critical security updates offered. Again, follow all prompts.

[I do NOT recommend installing IE7 via Windows Update.]

6. Make certain that Automatic Updates is enabled; cf.

http://support.microsoft.com/kb/306525

Additional References:

Free unlimited installation and compatibility support is available for Windows XP, but only for Service Pack 3 (SP3), until 14 Apr-09. Chat and e-mail support is available only in the United States and Canada.  

Go to http://support.microsoft.com/oas/default.aspx?gprid=1173 | select "Windows

XP" then select "Windows XP Service Pack 3"

5 steps to help protect your new computer before you go online

[clean install = new computer]

http://www.microsoft.com/protect/computer/advanced/xppc.mspx

Steps To Help Prevent Spyware

http://www.microsoft.com/protect/computer/spyware/prevent.mspx

HOW TO get WinXP Gold fully patched: http://groups.google.com/group/microsoft.public.windowsupdate/msg/3f5afa8ed33e121c

1a. Download & save the installer for WinXP SP2 to your desktop:

http://www.microsoft.com/downloads/details.aspx?FamilyID=049c9dbe-3b8...

[Yes, you can skip SP1]

1b. Download & save the installer for WinXP SP3 to your desktop:

http://www.microsoft.com/downloads/details.aspx?FamilyID=5b33b5a8-5e7...

2. Read & heed:

http://msmvps.com/blogs/harrywaldron/archive/2008/05/08/windows-xp-sp...

3a. Logged in as Administrator, if necessary, double-click on the saved file to install WinXP *SP2*.  Follow all prompts; be patient, and reboot twice when the install completes.

3b. Logged in as Administrator, if necessary, double-click on the saved file to install WinXP SP3.  Follow all prompts; be patient, and reboot twice when the install completes.

4. Do Resolution Method 2 here (trust me):

http://support.microsoft.com/kb/943144

5. Go to http://windowsupdate.microsoft.com | Install any required software then click on CONTINUE | Select CUSTOM and scan | Install any critical security updates offered.  Again, follow all prompts.

[I do NOT recommend installing IE7 via Windows Update.]

6. Make certain that Automatic Updates is enabled; cf.

http://support.microsoft.com/kb/306525

Addtional References:

Free unlimited installation and compatibility support is available for Windows XP, but only for Service Pack 3 (SP3), until 14 Apr-09. Chat and e-mail support is available only in the United States and Canada.  Go to

http://support.microsoft.com/oas/default.aspx?gprid=1173 | select "Windows

XP" then select "Windows XP Service Pack 3"

Protect Your PC!

http://www.microsoft.com/athome/security/computer/default.mspx

Learn how to protect your PC by taking three simple steps

http://www.microsoft.com/downloads/details.aspx?familyid=3AD23728-497...