What should the text displayed in the buttons for the noun genders be, and what wikicode should each of them output?
Oops, sorry, I missed your answer (never got used to liquid threads :) ) I don't understand your question.
Let me try:
m-an - masculine animate f-in - feminine inanimate, etc.
The rest must be straightforward.
So, there would be one button saying "masculine animate" which would produce the wikitext "|2=m-an"? Or "||m-an"?
Also, is "n" neuter? And what would be the text for the "-p" options?
I don't quite understand the usage of numbers here but m stands for masculine, f for feminine, n for neuter, an for animate, in for inanimate, p for plural (with nothing else). They can be used in any combination (like with other languages). p may appear on its own when gender or animacy is not known or not important. There can be nouns with more than one gender in the header.
Verbs can be impf - "imperfective", pf - "perfective", the other equivalent is usually provided, e.g. скрести. These two parameters and all genders are valid to all Slavic languages, although animacy may not be important for some genders in some Slavic languages, it is used for consistency and doesn't cause errors in Slavic languages. @CodeCat may give you some hints on gender handling modules. So, if you make it for Russian it can be copy-pasted for all Slavic languages but Serbo-Croatian uses different formats for imperfective/perfective.
Hm? There's a link in the search page, right after the link to create the page normally and the link to the Requested entries page.