I have an external blu-ray player of the sort that you usually connect to a regular TV or projector. Is it possible to use this one to watch films via HDMI on my laptop?
Unlikely - I don’t know of any laptop that has an HDMI input - usually you only find those on capture devices, and in that case the HDCP copy protection can be an issue.
So the only way is to connect this blu-ray player to a regular TV or projector? What about external blu-ray player that you usually find in a computer store? How would they have to be connected to the laptop and are they actually suitable for watching blu-ray films or rather made for storing data on blu-ray discs? I am asking because I had originally intended to watch blu-rays on this laptop and VLC seems to support blu-ray playback?
That would most likely be a Blu-ray drive as opposed to a full Blu-ray player. Those are usually connected via USB and require compatible player software. I know that VLC (if built with BD support) can play Blu-rays, but commercial titles are encrypted with AACS/BD+, and you need to provide the keys for those, which VLC cannot legally include.
There may be a licensed commercial BD playback application for Linux around (for DVD there were a couple as far as I remember).
Then I think I need to resort to online streaming services like MUBI or connect my blu-ray player to a video projector. Thanks a lot for clarifying these issues.