1. What kind of blog? A diary blog. Since 'diary' is describing the blog, keep it singular.
2. Number should remain singular. Think of it this way: When you saw the number of readers to your blog, did you see one number or multiple numbers? You only saw one number so it should be, "...the number of readers."
3. Every sentence should have: subject + verb. After who finished lunch? "After I finished lunch."
4. Keep the same verb tense. We are talking about the past so we would say, "I felt like writing again"
5. Verb tense. You listened to the songs in the past so it should be, "I listened to English songs."
6. Very minor grammar mistake. "I tried to learn the grammar."
7. Flip it. Should be "more fun." How much fun? more fun.
8. Close but switch the form of each verb. "it was more fun than trying to remember grammar from the book." And yes, for some reason you don't need 'the' in front of grammar here. I honestly don't know how to explain that lol.
9. Rewritten: "Listening to English songs is one idea for someone who is starting to learn English grammar."
One is describing idea so you don't need 'of an.' A better word here would be 'for' because this is an idea for someone to try. Similar to #8, change the verb formats and it works.