"kaj" shortened to "k"
I was looking up some words on vortaro.net and noticed in the definitions that it appears they are using just the letter "k" in place of the full word "kaj." I assume this is acceptable? Is it similar to how the final "o" can be replaced with an apostrophe? I've just never noticed or seen it anywhere else but on vortaro.net.
For example, here is the definition for "restoracio."
"restoraci/o. Ejo, kie oni povas kontraŭ pago manĝi k trinki"
My impression is that k. for "kaj" in Esperanto is in broader use than, say, s.o. in English for "someone". Maybe that's because a greater proportion of Esperanto speakers actually sit down and read a dictionary cover to cover - who knows. (Yes, it happens.) In any event, shortening kaj to "k" is more appropriate in Esperanto than using an ampersand (&), which is occasionally seen as well.
Fun fact: the symbol "&" comes from a stylized cursive drawing of the Latin word for "and."
Why can't you use an ampersand in Esperanto?
I think a better question would be - why would you think that you should be able to? On what basis do you suppose that the practice is international? For comparison, look at the German Wikipedia article on Ampersand. Most of the focus is on the use of the ASCII symbol in programming, and it says explicitly that it's much more common to write "u." (und) instead of using a symbol.
I also found it interesting that there's a symbol for the Greek version of the word kaj that looks very much like "k.".
Mi scias ke mi estas malfrue, sed jen la ligilo:https://en.wiktionary.org/wiki/Category:Esperanto_abbreviations
As in any dictionary, abbreviations are used for certain things to save space. You wouldn't necessarily use these in regular writing and certainly not in formal writing, but it's not "against the law" to use them in informal writing. "k" for "kaj" is one of those things.
There is also quite a long list of common abbreviations, like k.t.p. for "kaj tiel plu", and I've heard people use it in conversation as "ko-to-po", but I prefer to say the words out fully. You might come across things like that from time to time.