I heard an unsourced claim about wounds, bruises and internal bleeding healing much worse in 0g conditions than in normal gravity. Is it true? And if so - could you provide a quantitative comparison, how much worse it is?
It's a lot worse in space than on land. Quantitative studies on wound healing in zero g haven't really been done as of about 2013 (the latest paper I could find). However, there are some sources that explain some of the issues. The first one, here, talks about how astronauts say that minor wounds don't heal until they are back on Earth (sorry, the exact definition of "minor" is missing from that article, but this article describes it as a "small nick"). Another source, here, uses the number 100mL/min, which is sourced in that article as being something of a point of no return where the crew member probably would not survive, presumably due to blood loss as clotting won't happen. That article also talks about some practical issues of how blood would spray in the spacecraft or potentially pool around the wound, obscuring vision and making surgery much more difficult. The original article for the 100mL/min claim is here, and it has a bunch more information with specific numbers about mortality.
The latest paper I've been able to find here is behind a paywall, but the abstract states that little is known about zero-g wound healing.