Understanding the modes

[xeruf]

Does custom mode assume all listed files are part of the same album? That is not quite clear from the manual.

Similarly for easy mode it does not mention whether it writes the tags to the files automatically.

[complexlogic]

Does custom mode assume all listed files are part of the same album?

If you enable the album gain calculations with -a, yes.

Similarly for easy mode it does not mention whether it writes the tags to the files automatically.

Yes, the Easy Mode is set to tag mode 'i' by default, which writes tags.