I have a bad news. I have bad news.

We almost never say "a news", we would say "a piece of news" or something along those lines. However, in this case just "news" with no article fits the best.

I have a bad news. I have bad news.

"Bad news" is not something that you can quantify/count, so you don't need "a" as a preposition.

I often drive on a certain highways. I often drive on a certain highway.

Given later sentences it makes sense to specify that you're talking about a particular highway.

One of the section was is under construction fromstarting this week. One of the sections is under construction starting this week.

Here it makes sense to express this in the present tense if it is still under construction.

One of the sections was under construction fromthat started this week. One of the sections was under construction that started this week.

There are multiple sections on a highway, so you need "s" at the end to indicate that it's plural. To say the contruction began this week, you would say "That started", because it specifies when the construction started.

It takes more 30 minutes tor an hour longer when I use it to go to my customer in morning. It takes me 30 minutes to an hour longer when I use it to go to my customer in morning.

I usually take more than 30 minutes or an hour when I use it to go to my customer in morning. I usually take more than 30 minutes or an hour when I use it to go to my customer in morning.

You can use "usually" to say it's a habit. You also need "than" to talk about quantities. Ie "more than 30 people"

In addition, it will last thise entire month. In addition, it will last the entire month.

Adding a word like "entire" or "whole" emphasises how much time you think it is.

In addition, it will last until the end of this month. In addition, it will last until the end of this month.

you need to specify a quantity when you use "last" as a form of time ie "it will last all of this month". "it will only last a few weeks"

WIs there anyone who likes it? Is there anyone who likes it?

Adding this extra part at the start emphasises the rhetorical nature of the question.

Who likes itconstruction? Who likes construction?

It sounds more natural to repeat construction here so the reader understands what you're talking about

The worst month hads started. The worst month has started.

Present tense makes most tense since the month is still in-progress.

The worst month hads started. The worst month has started.

Your story is in the present tense, so you should keep it consistent.