@Arawaraw
You may find it helpful to think of “where are you from?” for “taga-” and “where did you come from (recently)?” for “galing sa”.
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The answer to your question about "mayroon" and "may" is not that simple: 🤕😅
Both “may” and “mayroon” can mean either “to have” or to indicate the existence of something. “Mayroon” is also written informally as “meron”. Their opposite is the word “wala (none)”.
(Note: When syllabicating “mayroon”, we pronounce “may” as “mai”, but when we speak, it would sound more like “meyroon” which is why its short and informal form is “meron”.)
Remember the following:
I. The linker “na” is needed after “mayroon” to link it to its object.
II. Both can be used to express the same thing, but it’s not always a case of simply replacing one word with the other. That is, when used in a sentence, the structure of the sentence may have to be modified to make it grammatically correct.
III. “Mayroon” can be used just by itself, but you can’t do that with “may”.
Take note of how they [I, II, III] apply in the following examples:
1) When the actor/subject is a noun:
May trabaho si Mary. = Si Mary ay may trabaho. = Mary has a job.
Mayroong/Merong trabaho si Mary. = Si Mary ay mayroong/merong trabaho. = Mary has a job. - “Mayroon/Meron” becomes “mayroong/merong” because the linker “na” got attached to it. (mayroon NA trabaho = mayroonG trabaho) [I]
Q1a: May ginagawa ba ang nanay mo ngayon? = Is your mother doing something right now?
Q1b: Mayroon bang ginagawa ang nanay mo ngayon? = Is your mother doing something right now? (ba na = bang – the “na” after “mayroon” gets attached to the question word “ba” instead) [I]
2) When the actor/subject is a pronoun, its position changes with “mayroon”:
May kotse siya. = Siya ay may kotse. = He/She has/owns a car. - When the sentence begins with the predicate, the pronoun “siya” comes AFTER the object as was the case with the nouns above.
Mayroon siyang kotse. = Siya ay mayroong kotse. = He/She has/owns a car. – The pronoun comes BEFORE the object. (mayroon siya na = mayroon siyang) [II]
Q2a: May gagawin ka ba bukas? = Are you doing something tomorrow? (“ka ba” comes AFTER “gagawin”)
Q2b: Mayroon ka bang gagawin bukas? = Are you doing something tomorrow? (“ka bang” comes BEFORE “gagawin”) [II]
Other examples:
Q: May trabaho ba si Mary?
Acceptable positive answers: (You may also opt to begin each answer with “oo [yes]”.)
A1: Oo, may trabaho si Mary; May trabaho siya.
A2: Mayroon/Meron. (“Mayroon” can stand alone.) [III]
A3: Oo, mayroong/merong trabaho si Mary; Mayroon/Meron siyang trabaho. [II]
Q: Mayroon ka bang gagawin bukas? [II]
Acceptable answers:
A1: Oo, mayroon/meron. [III]
A2: Mayroon/Meron akong gagawin bukas. [II]
A3: May gagawin ako bukas.
Lastly, please be aware that “may” does not always mean “mayroon”. It can be:
1) used to indicate a fuzzy location of something.
Nasa may ibaba ng hagdan ang pusa. = The cat is somewhere near the bottom of the stairs.
Sa may bandang kanan ng TV mo hanapin ang remote control. = Look for the remote control somewhere to the right of the TV.
2) used as a prefix, similar to the “mag” or “um” prefix, but more intended to refer to the creator/fabricator of something.
Si Jack ang maygawa nito. = It was John who did this. (This could mean that John created a significant object or event. “Maykagagawan” is more often used when the event turns out to be problematic.)
Sino ang maysabi? = Who said so? (Often used instead of “sino ang nagsabi?” when one doubts the accuracy of a given statement or the reliability of its source.)
by: 
