Many new shops are opening up in my neighbourhood.

[Jit833]

1) Many new shops are opening up in my neighbourhood.
2) He tried to show off by sliping something irrelevant into our conversation. For example, when you ask him how he was, he will tell you he is a billionaire.

I hope the sentences above make sense. Hope somebody can correct my mistake if there is any? Thank you do much.

[Grumpy]

1) Many new shops are opening up in my neighbourhood.
2) He tries to show off by slipping something irrelevant into your conversation. For example, when you ask him how he is, he will tell you he is a billionaire. Or: He tried to show off by slipping something irrelevant into our conversation. For example, when I asked him how he was, he would tell me he was a billionaire.

I hope the sentences above make sense. Hope somebody can correct my mistakes, if there are any. Thank you so much.

Your first sentence is fine.
In your second passage, you are mixing up your tenses.