Reimbursable expenses

Let's break this down into parts.

"Will I have Expenses and income at the end, or I will go to zero because it offsets?"

You want the Reporting to show the Net. Not the account details. You want Travel Gross and you want Income gross.

"We are Company Inc who has almost all expenses reimbursed by the other company."

"Reimbursed" is not the Accounting. It's a Process. Are you describing Sales to a Customer? Did you travel for that customer?

"How should I record transaction?"

What you show is Accounting. You should be using Items.

"Do I record a bill,"

You use bill, because you owe that to someone and did not Pay. For instance, the Airline probably had you Pay = enter Credit Credit Card Charge. There is no Bill; the Airline doesn't send you a Bill for you to pay later. Or, you paid by Checking already; that is Enter Check, even if Paperless via Debit card.

"for instance Travel expense,"

Make Items, if you intend to include Customer Names on the details. Service items for labor is typical; nonivnentory type, for materials such as Supplies or other products you ordered on behalf of that customer name. I use Other Charge Type for Airfare, Lodging, for Shipping, for Postage.

Tracking the Customer = direct, and the Billable to them or not is the next Option.

"then create an invoice with  what?"

When you are ready to Charge them all the Billable costs you incurred, you make Invoice and use Add Time & Costs, to select the Billable charges. If that Travel is part of  Fixed Bid Contra,t then you Job Track it, but that is Not Billable. You will be invoicing them for the Contract Amount they owe you.

And Two Sided Item = mark that this is something you incur and charge back. That gives an Expense account link and an Income account link.

Example:

You hire subcontractors, so the Service Items might be Graphic Artist and Photographer and even Model. They all link to the same one Contract Labor expense account and to the same one Sales Income account.

"Can I do something as attached file, or this is something different?"

So, do not post to Accounts as your image shows. See to the Right of the Blue button for Account? Click on Item. Use that view. Now, you get to include Quantity, you are creating a Cost that will be related to the Sale, you have Item Profit and Job reporting data.