-We have a couple of PCs in office but I am not sure whether they work well.

I need to ask Aldo that which one would suit Mr Ozgun.

When do you plan ton having him start him working aton the Gulf Project?

-We can count the value of the first invoice for the next service of the BAC Company.

He issues a 70k USD invoice each month onfor this business.

-We underpaid by 229 EUR by short last time.

Could you please compensaterefund the residual amount?

Because these companies does not pay invoices on time.

And unpaid invoices drive acause troubles throughout the VAT refund process.

This way, our VAT refund process canwill be easier than the current statuprocess.

-We have a couple of PCs in the office but I am not sure whether they work well or not.

When using "whether", you need to provide both ideas to compare, usually with an "or": "Whether there is rain or not" "Whether they work well or not"

I need to ask Aldo that which one suits Mr Ozgun.

We don't use "that" to connect after "I need to <something>":

"I need to ask him what he is doing."
"I need to ask her which one she likes best."

Using "suit", it requires the "s":
"It suits you well!"
"Which one suits me best?"

-You agreed (with*) Mr Thomas on the working conditions.

*It's not clear from context if you are talking to Mr. Thomas, here, or if you are telling someone they agreed with Mr. Thomas.

"You agreed, Mr. Thomas, on the working conditions." if you are speaking to Mr. Thomas.
"You agreed with Mr. Thomas on the working conditions." if it is a statement to someone else

When do you plan to start him working aton Gulf Project?

-We can count the value ofsettle the first invoice for the next service of BAC Company.

It is understandable but we would not say "count the value of the first invoice". Instead we would say "We can settle the first invoice for the next service of BAC Company."

He issues 70k USD in invoices each month on this business.

-We paid 229 EUR by shortwere short by 229 EUR last time.

It's not entirely clear what "by short" means here. Do you mean you paid less than owed? If so, use "We were short by 229 EUR last time."

-We should invoice to BAC, DAC, and BBC at the end of each quarter.

Because these companies does not pay invoices on time.

We try not to start sentences with "Because" unless they are quite lengthy. Merge this sentence with the previous one. Also, "does" would be for a singular company. With plural companies, use "do".

And unpaid invoices drive acause trouble throughout VAT refund process.

"Drive a trouble" is not correct. It is correct to say "cause trouble" instead.

This way, our VAT refund process can be easier than as it currently statunds.

This is tricky but 'as it currently stands' is a good phrase to remember for this situation. You can use it at the beginning of a sentence, too:

"As it currently stands, the VAT refund process is difficult."