I would like to create multiple installations of DNN, one for each website and have all of them use the one same database.

1) Is this a good practice?

2) Are there any downsides to doing this?

3) Is having a database for each website more efficient? Faster? 

4) When all installations of DNN use the same database are there problems with concurrency?

It depends on how you're planning on doing it. I think you can get away with it if you're using a separate database owner and/or object qualifier for each install but is there a particular reason you want multiple installs using the same database instead of one install with multiple portals?

1) I leave whether it's good practice or not for others with more hosting experience to answer.

2) If you do it like I suggested then everytime you need to update a module/DNN version you'll have to do it for all the different database owner/object qualifier instances.

3) Depends on the website. If they're really busy, under a high load then I'd go with separate databases. Otherwise I just use multiple portals on one instance.

4) See my answer for number 2. I really don't think you can have multiple installs using the same database without changing either the database owner or object qualifier but I've also never tried to do it that way either.