I do think they ought to have a period in English too, but it also wouldn't surprise me if some style sheet somewhere now preferred them without.
I can't confirm that ff. is italicized; in fact, I don't think I've ever seen it italicized.
Some sort of cautionary marking for the ones that are now uncommon might also be helpful.
Many modern style guidelines now advise against using the single f. at all, because it's clearer just to put 301-302. Even for the double ff. it's preferable to give an exact page range if possible.
To my knowledge, I've never seen et seq. used, much less et s(e)qq.; I would guess that it's largely either obsolete or obsolescent, though it might have been slower to disappear in legal and/or BE circles.
I agree that if you wrote out something in full in English, it should probably be 'and the following page(s)'; however, since 'page(s)' is usually already understood, I usually think of it as simply 'and following.' Somehow it's the 'the' that seems a bit off.
I also agree with Chicago that there should not be any space preceding ff. or f., that is, between the page number and the abbreviation, but I'm not sure you can convey that in a dictionary entry. Basically, anyone working with reference conventions needs to own a complete source, like Oxford, Chicago, MLA, or all of the above.
There have been several discussions on these over the years, some probably with more citations from typical authorities.