Verified answer

The anticipation is intensifying?

No one would ever say that in English. It sounds really stuffy.

I would say,

I ordered some DVDs. I'm so excited that I can barely wait for them to come in.\

-or-

I ordered some DVDs and am so excited that I can hardly wait for them to arrive.

For the second sentence, I would say simply that:

Having an accent doesn't affect my proficiency in English.

(I left out the ability part because everyone has the same ability of being proficient in English. The only thing that would be affected by a heavy accent is the proficiency)

The third, I would word thus :P :

When I started seeing Johnny, he kept on making excuses (about/as to) why he couldn't hang out with my during the day. I didn't think anything of it. But, it became a pattern and I finally realized that he was only interested in sex.

or

It was starting to become a pattern when I realized that he was only interested in sex.

These are the corrected sentences.

1) I ordered some DVDs and and I can't wait for them to arrive, since the anticipation is intensifying at this point.

2) Having an accent doesn't affect my ability to be proficient at English.

3) When I started seeing Johnny, he kept on making excuses as to why he couldn't hangout with me during the day and I didn't think anything of it. However, it started becoming a pattern and I finally realised that he was only interested in sex.

1) I ordered some DVDs and and I can't wait for them to arrive because my anticipation is intensifying now.

2) Correct

3) When I started seeing Johnny, he kept on making excuses as to why he couldn't hang out with me during the day, and I didn't think anything of it .However,it started becoming a pattern and I finally noticed that he was only interested in sex

It needs work for sure, but it isn't too bad. Relax. You write better than a lot of people whose first language is English.