"May" precedes nouns, verbs, and adjectives
Example:
May aso dun sa kanto. (There's a dog at the corner.)
May tinda pa sila dun. Bili. (There's still some being sold. Hurry.)
May mga magagandang chix dun pre. (There are some beautiful girls there man.)
"Meron" is a verb, I think (because of state verbs). It describes the presence or absence of something. Meron in its root form can be used to answer questions.
Example:
May tinda ba sila dun? Meron yan. (Do they have these for sale? Yes they do.)
Meron can also be followed with adverbs.
Meron ngayon nagbabarilan sa may kabilang barangay. (There is a firefight currently happening at the nearby district.)
- may ngayon won't make anysense
"Meron" can be modified with affix -g, and the word_na_
Merong nagbabarilan sa may kabilang barangay. (There is a firefight at the nearby district)
Ayoko merong angswang dun. (I don't want to there's a ghoul(?) there.)
- merong and may can be used interchangeably
Meron na namang nakalampag sa bubong, kunin mo yung itak. (There's a banging on the roof again, get the bolo.)
- in this case may could be use with meron but you have to move the adverb na naman.
May nakalampag na naman sa bubong, kunin mo yung itak. (Something's banging on the roof again, get the bolo.)
"May" could be interchange with meron if added with -roon.
Mayroong may gusto sayo. (Someone's got a crush on you.)
I'm not a linguist by any means but these are the things that I have observed as someone speaking the language.