As the author of StackApplet, I will try to answer your questions:

1. Whenever one clicks on the "Ask Ubuntu" in the StackApplet's menu it opens http://askubuntu.com/users/recent/### (where ### is the user's id number), but there is no such page here.

Yes, this page was removed and is no longer available. I have corrected the URL in newer versions of StackApplet. Based on your post, I'm guessing you are using StackApplet 1.4, which is the current stable version. Version 1.5 is almost ready for release and is considered very stable on Ubuntu. You can find it in the StackApplet PPA here.

2. Is it possible to follow new questions being asked here using the StackApplet?

No, this is planned for StackApplet 1.6.

As the author of StackApplet, I will try to answer your questions:

1. Whenever one clicks on the "Ask Ubuntu" in the StackApplet's menu it opens https://askubuntu.com/users/recent/### (where ### is the user's id number), but there is no such page here.

Yes, this page was removed and is no longer available. I have corrected the URL in newer versions of StackApplet. Based on your post, I'm guessing you are using StackApplet 1.4, which is the current stable version. Version 1.5 is almost ready for release and is considered very stable on Ubuntu. You can find it in the StackApplet PPA here.

2. Is it possible to follow new questions being asked here using the StackApplet?

No, this is planned for StackApplet 1.6.