How many backlinks per day is safe?

Backlinks almost never have a limit when it comes to how often they can be used, or how often you use them. The only thing that matters is the overall quality, and the credibility of backlinks.

Any one company or entity could reference websites, and use them as a backlink. But that's where credibility when referenced to search engine optimization comes into play.

Say for example, you referenced a ton of websites that are known for a very hard to use interface, or are known to be quite difficult to use. Search engines will take this into account based on how long users stay on that site, and that might rank your search lower, if it shows it at all due to this.

In short, the only thing that matters on the amount you use, is if they are credible, and reliable sources that are simple to use, and don't have a reputation that might damage your own. I mean after all, ten thousand good backlinks are definitely going to look better on you than nine thousand good back links and one thousand bad ones. So as long as you use the correct ones there is absolutely no limit.