The worker start his work at around 9 am again. The worker start his work at around 9 am again.

The worker started his work around 9 am again. The worker started his work around 9 am again.

The worker start his workarrived around 9 am again. The worker arrived around 9 am again.

You used "started" in the first and second sentences. To avoid this repetition, I suggest a verb that relates specifically to time.

He started toby takeing down the upper cabinets and reattached them a little bit lower. He started by taking down the upper cabinets and reattached them a little bit lower.

"started by" gives the nuance that this is the first thing that this person did. while "started" would simply means that he has begun that task at that moment.

He started to taketook down the upper cabinets and reattached them a little bit lower. He took down the upper cabinets and reattached them a little bit lower.

He started to take down the upper cabinets and reattached them a little bit lower. (This doesn't sound right to me.) He started to take down the upper cabinets, and he reattached them a little bit lower. (IDK if this fixes the problem.) I like @Lionel's suggestion of "he started by," but I'm not sure that it aligns well with "he reattached." I tried some variations, but I couldn't decide if they were grammatically correct! He started by taking down the upper cabinets and reattached them a little bit lower. (?) He started by taking down the upper cabinets, and he reattached them a little bit lower. (?) He started by taking down the upper cabinets; then he reattached them a little bit lower. (?) He started by taking down the upper cabinets, which he reattached a little bit lower. (?) When I am confused like this, I choose a structure I know is correct!

Around noon, our kitchen project design manager stopped by my home and showed me some tile samples. Around noon, our kitchen project design manager stopped by my home and showed me some tile samples.

Around noon, our kitchen project design manager stopped by home and showed me some tile samples. Around noon, our kitchen project design manager stopped by and showed me some tile samples.

"Home" is not necessary. "Stopped by" is a common expression by itself, with the "here" implied. You could also say, "stopped by the house."

Around noon, our kitchen project design manager stopped by home and showed me some tile samples. Around noon, our kitchen project design manager stopped by and showed me some tile samples.

"stopped by" and "came over" (stop by & come over) both imply that you are in a place, and the person in question is joining you there

We had already had talked about it before and she just wanted to confirm it. We had already talked about it before and she just wanted to confirm it.

or you can also say "We had already discussed it...."

We had already had talked about it before and, but she just wanted to confirm it. We had already talked about it before, but she just wanted to confirm it.

talked about it OR discussed it "but" is better than "and" because the second part is surprising, given the first part.

We had already had talked it before andabout tiles, but she just wanted to confirm itmy choice. We had already talked about tiles, but she just wanted to confirm my choice.

You don't need "already" and "before" in the same sentence. One is enough. "it" doesn't clearly refer to something in a previous sentence. The closest thing is "tile samples" In speaking, you could use "we talked about it before" meaning "we talked about that topic," but in writing it's best to be precise, so that your reader doesn't have to pause and figure things out.

I choose a simple, white, and glossy square tile. I chose a simple, white, and glossy square tile.

for past tense consistency

I choose a simple, white, and glossy square tile. I chose a simple, white, and glossy square tile.

I don't like to overcorrect punctuation for language learners, but really this should probably be "simple white

I choose a simple, white, and glossy square tile. I chose a simple white, glossy square tile.

Tomorrow the, another project manager will come here and install our countertops. Tomorrow, another project manager will come here and install our countertops.

Tomorrow the another project manager will come here and install our countertops. Tomorrow another project manager will come here and install our countertops.

Tomorrow the another project manager will come here and install our countertops. Tomorrow another project manager will come here and install our countertops.

"the other" (if there are two) or "another" (if it is just one more and we don't know the total number)

I am going to talk about the plumbing and electrical problems with him. I am going to talk about the plumbing and electrical problems with him.