||Just to be sure:
1) Have you unzipped and placed the .avx file in c:\esri\av_gis30\arcview\ext32\ ?
2) In AV, when you click File...Extensions does the extension appear in the list of available extensions? Always? Sometimes? When you say "when I go to extensions in arcview (1) the extension is there but I am not able to activate it (2) the extension is simply not shown" do you mean that sometimes it's there and sometimes not, randomly?
3) When you click on the extension's name, does the description of the extension appear in the box at the bottom?
4) Can you click the checkbox? If not, does it show a little circle with a line through it as the icon when you hold the mouse over the checkbox?
5) If you can click the checkbox, does the extension load without any errors? Does the extension work?
6) Does this problem occur with ALL extensions that you download? How about with extensions that came with ArcView? Try downloading another common extension like XTools and see if the problem is the same. What extension(s) are you having the problem with?
7) if you click the Add Themes button and type $AVEXT in the Directory: box at the top and hit ENTER; does it go to the directory where you are keeping your extensions? If so, try typing $USEREXT in that box (it'll probably go to C:\temp or something) and try placing the .avx file in that directory. These are the places AV looks for extensions.
8) Does the Crystal Reports problem happen exactly the same way as the other extension problems, or is it different?