Old british possibly educational alien kids show

I also kind of had similar memories of a show like this back in elementary school (even though I can't remember the name of the show) when I was shown two episodes where the alien crashes on Earth during Halloween time and the kids mistake him being a kid in a costume and he eventually becomes friends with one of the kids who gets picked on a lot.

The other episode was when the kid goes to his grandmother's house and at the same time gets picked on by a bully at his school. He calls out for his alien friend but he doesn't come immediately because space travel is slow. When he finally arrives back to Earth to help his human friend, he stops the bully from harming him and make him say that he is sorry for what he had done to his friend. After the bully apologizes, the alien reassures his human friend that he will try to be there for him.

I'm sorry if I am not much help to the show that you are trying to look for, I just got a little nostalgic from the description you gave and made me recall a show that I haven't seen since elementary school but I still remember a few details about it. But from what I can tell, the show that I remembered as a kid doesn't match up from what show you remember.

Katie and Orbie ?
en.wikipedia.org/wiki/Katie_and_Orbie
www.youtube.com/watch?v=6zHcOJ6zW5w

In my case, it was an animated show.

Here is the Wikipedia article about Pet Alien: en.wikipedia.org/wiki/Pet_Alien

It seems to almost perfectly match up with what cruggers122 remembered as it does involve the characters living in a lighthouse by the sea (though the article says it was an American made computer animated series instead of being made by the British and it did air on Cartoon Network for 52 episodes between January 23 to May 26 in 2005).

However, in my case of what I remembered, the show I remembered was 2D animated and appeared to be made much earlier than I watched it in the media center sometime in 2007 (I don't remember the decade it was made in).

Unless cruggers122 can confirm this to be true, it looks like Pet Alien has to be the closest answer for what he remembers for right now. 

Ooops, I should have clarified that I am not cruggers122 and I'm just a guest who wanted to be involved in this discussion and remember a show that I recalled seeing a show being similar to his (possibly Pet Alien). You're not wrong about what you found for crugger122, though.