Installing Broadband for My New Apartment Installing Broadband for My New Apartment

"Install Broadband for my new apartment" is an order, which makes it a little odd for a title. "Installing" instead of "install" makes it just describe the activity, which is more natural for a title.

Installing Broadband forin My New Apartment Installing Broadband in My New Apartment

I applied for broadband service at a China Unicom center lasyesterday at noon (?). I applied for broadband service at a China Unicom center yesterday at noon (?).

I applied for broadband service at a China Unicom center lasat noon yesterday. I applied for broadband service at a China Unicom center at noon yesterday.

I assume you mean noon yesterday. I’m not familiar with the expression “last noon.”

However, it was understandable, as the engineers were extremely busy on weekends, and the engineer had informed me in advance that ithe would be late due to a minor issue with his last client. However, it was understandable, as the engineers were extremely busy on weekends, and the engineer had informed me in advance that he would be late due to a minor issue with his last client.

"it" for people is often considered rude (with the exception of some LGBT/nonbinary people who choose it for themselves) Generally you'd use the appropriate gendered pronouns (he/she) or else use "they" as a fallback for a person of unknown or unspecified gender.

However, it was understandable, as the engineers weare extremely busy on weekends, and the engineer had informed me in advance that it would be late due to a minor issue with his last client. However, it was understandable, as the engineers are extremely busy on weekends, and the engineer had informed me in advance that it would be late due to a minor issue with his last client.

I changed “were” to “are” because you seem to be describing their situation on weekends in general. If you meant to describe last weekend specifically, you could say, “…as the engineers were extremely busy this weekend….”