Yes, there are several wearing verbs for different items, נועלת נעליים, גורבת גרביים, חובשת כובע, עונדת תכשיט, מרכיבה משקפיים, עונבת עניבה, these are the ones I can remember now. Other items go with the default לובשת. Not all speakers bother with all of those, some just use לובשת for all. I would estimate that נועלת and גורבת are the most common.
The word for the wearing action is sometimes related to the worn item like: Wearing a shoe == נועל/ת נעל Wearing (or putting on) a sock == גורב/ת גרב Wearing clothing == לובש/ת לבוש
That's because you don't use Nikud. It's a convention that without Nikud יי represents the sound AYI while י represents the other sounds related to it.
But why the plural of na'al is not the regular form na'alim, but rather na'alayim? Is it an irregular plural?
Things that go in pairs get the suffix -ayim, like yadayim, raglayim, eynayim, oznayim, shinayim, michnasayim, garbayim, na'alayim. Even the day after tomorrow, which is two tomorrows from now is macharatayim (or actually mochoratayim, but anyway everybody says machratayim).
Why "You are wearing A shoes" does not work? I'm not native english speaker and can't understand difference between "you are wearing a shoes" and "you are wearing shoes".
"A" is only used for singular, not plural.
• You are wearing a shoe (a single shoe) • I have a book (again, just one)
• You are wearing shoes (more than one shoe) • I have books (multiple books)
Another option in English is to use "pair", which is a set of two. • You are wearing a pair of shoes (a single pair of two shoes) • You are wearing pairs of shoes (more than one pair)