How to create a faux project remaking an existing brand -

This would be a violation of the name brand's intellectual property, design and copyright.  I wouldn't risk it.  That could pose a serious legal problem for you. Courts always side with copyright & property holders. 

Brands are fiercely protective of their identity & recognition. Even fake & parody ads can have legal consequences. As in the case of

Jack Daniels vs Bad Spaniels trademark case

https://www.sullivanlaw.com/viewpoints/in-jack-daniels-v-bad-spaniels-trademark-case-supreme-court-holds-parody-products-on-a-short-leash

Best advice, stick with mythic products and mythic names. Don't try to copy real ones.

Many larger companies often have vector-based versions of their logos contained within PDF files they post online. It could be anything such as corporate annual reports, product brochures, manuals, brand guidelines documents, etc. You just have to do a bit of web searching. The PDF can be placed in Illustrator and run through the Flatten Transparency dialog box to outline any embedded fonts. I've had to use this tactic from time to time to get logos for sign design projects when their people couldn't manage to tell the difference between the first JPEG they found on a computer to something that's actually useable. Other companies are better (they send proper logos and brand guidelines documents).

I am NOT a fan of the Brands of the World web site and other similar sites. Some logos posted there are seemingly legit. But there is a lot of fan-reproduced copies of logos posted there that are not accurate. In addition, many companies update their brands from time to time. The Brands of the World site won't always have those latest versions. I very much prefer getting corporate logos directly from the company or extracting logos out of one of their own PDFs online.

The sample ad campaign idea sounds like it falls under the legal category of fair comment.  If you're not getting paid for creating the project or using that company's logo to make money from it, such as selling kinds of merchandise, you should be in the clear. Still, I would probably not post such work online where it could be seen by lots of people. It could be misunderstood as being actual commissioned work done for that company when it isn't.

Also I found an interesting reddit on this! Apparently it's called Spec work! You learn something new everyday. https://www.reddit.com/r/graphic_design/comments/lbvh3/is_it_legal_to_create_fake_publication_design_for/ 

So this is just for your portfolio and you will clearly communicate that you do not work for them? I don't know how that company usually reacts to fan art. So basically you have to take into account what Mylenium said.

You have no chance qhatsoever to get the font.  The logo wmight already be in collections such as Brands of the world.

Maybe just ask that company if this would be OK with them? 

Or design a new branding for them in the way you think would be appropriate?

And what happens when they find out or artwork from your portfolio leaks? They'll kick your deriere with those robust boots and sue you over false representation of their trademark. Unless you actually worked for them and have references from a real campaign, this is a big no-no. A fitting example would be when Nike came down on 3D artists in the mid 2000s when they sculpted their shoes in ZBrush and sold the 3D models.... And if you know the product well, it should not be difficult for you to create your logo "in the style of X" rather than using their actual branding.

Mylenium