Oh I'm sorry I clearly misunderstood the question.

I have not seen any studies or testing done on this, but I have to assume that they are ignored by spiders entirely. I certainly don't think they are more damaging than a 404 would be. A 404 tends to be ignored and only registered if a certain amount of time passes and the page is still not found. Google doesn't make it a habit to instantly remove URLs unless you ask them to.

At the very worst, the 403/404 error would de-index that particular URL but this should not affect the rankings of your other pages and your actual site. And I think it'll take at least a good 30 days before Google will stop crawling those. That said, it shouldn't be crawling them at all if there aren't any links pointing to them either internally or externally. And if there are links pointing to the pages in question, you should be redirecting them via 301. That is of course if they are links you want.

Hope this was more helpful.

403s are forbiddens that are only returned if the server is told to block access to the file. If the site had been built with Wordpress in the past and has directories that match current directories, it may be returning 403 errors as the sitemap differs..

This is hard to explain and I think my wording it is confusing.

Say you had on your old site domain.com/blog/ and that went to your blog's index but now you have domain.com/blog/contents.html as your index. Well the /blog/ command would be trying to pull a directory and your server would normally automatically return a 403 forbidden for such requests.

Does this make sense? Might not be what's going on, but it's one possibility.

"Do you recommend scrapping the subdomain in such an instance and hosting them all in the main domain in a folder?"

Yes.

"Would that impact on page load and speed?"

No.

This PDF is a perfect example of why not to do this, but the same can be said for images. Say you create an awesome infographic that people start linking to/sharing, and it's sitting on your subdomain. There goes your SEO benefit, much like you're experiencing with this PDF.

If you have the right hosting service, none of this should impact performance. Looking into a CDN will help for sure. I've heard good things about cloud flare, for example.

"My developer says it is better to keep images, pdf, css in the subdomain. I see his point"

You do? I sure don't. That sounds ridiculous to me and I see absolutely no reason why this should ever be necessary. I'd be surprised if anyone else did.

Your original plan was the right one; move that pdf to your main domain in a pdf folder or whatever and redirect the original URL right to it. That's the way to go, for sure. If you want to build it as an HTML page that's fine too. I personally would do that if it were an option mainly because I can't stand PDFs. But that's me.

No reason you need to have pdf, css, and images in a subdomain. That's silly.