Is it possible for a firm to develop a design without their consent?

Question

Design

One airline has a very terrible website, in terms of design. As a designer, I want to develop a template for free and contact the management in the future. The chances that they will accept it are minimal, since they will hardly make up a new layout. But in this case, I can put it on my site without further consequences, because there is their logo and so on.

Answer 1

As a designer, you can change the logo, name and contacts of the company. And put it on your site without their permission.

Answer 2

Make a redesign and send them the logos and, for example, write an article in the CPU (they have interesting articles on this topic: one , two , three ).
And in the portfolio lay out the design without logos.

Answer 3

You can design for a company and post your work with their logo and all the information you put in the design. Only in the description of your design, indicate in text that this is a creative project, and an idea how to improve the look of the company. If you're really worried, you can list what part of the work is yours, for example: color palette development, prototype creation and website design.
Look at behance, there you can often find author's redesigns of facebook, youtube, twitter, and designers use both company logos and even corporate colors, indicating that their work is only a new concept and new design.