@calingaerta
The explanations given by Daoxin are correct, but there are also some exceptions based on actual usage.
RE: "Magandang babae" would mean "The woman is beautiful"
No. It only means "beautiful woman".
Maganda = beautiful; babae = girl, lady, woman, female
As Daoxin mentioned, when a noun is modified by an adjective, we need the linker "na" between the two words to establish their relationship. (The same thing applies when relating an adverb to a verb). This "na" functions like a "that/which is" connector.
Also, when the word before the "na" ends in a vowel, normally, that "na" gets attached to that word as "ng".
"Maganda NA babae" [beautiful (which is a) woman = beautiful woman] becomes "magandaNG babae".
"Tumakbo NA mabilis" [ran (that was) fast = ran fast] becomes "tumakboNG mabilis".
Most of the time also, the position of the noun/verb and its modifier may be interchanged and would still mean the same thing. Hence, "magandaNG babae" may be expressed as "babaeNG maganda" and "tumakbong mabilis" may be expressed as "mabilis NA tumakbo". Since "mabilis" ends in a consonant, the "na" stays as is.
So, the "ng" at the end of "magandang" stands for "maganda na" and not for "maganda ang".
RE: "Ang mangandang babae" would mean "The woman is the beautiful one"
Also, no.
"Ang" is the equivalent of "the". "ANG maganda" means "THE beautiful (one)" and "ANG babae" means "THE girl/lady/woman/female".
Since "magandang babae" is "beautiful woman", therefore, "ANG magandang babae" is "THE beautiful woman".
RE: And the -ng added to maganda always acts as "ang" and is not only there as linker?
No, it is there not as "ang", but as the linker "na".
Daoxin gave you "Ang babae ay maganda" as the correct translation of "The woman is beautiful". "Ang babae" is the subject and "ay maganda" is the predicate.
However, in a Filipino sentence, the positions of the subject and predicate are usually interchangeable and transposing them also does not change the meaning of the sentence.
Subject-predicate: "ANG babae ay maganda" = THE woman is beautiful
Predicate-subject: "Maganda ANG babae" = THE woman is beautiful (The "ay" is omitted when a sentence is in the predicate-subject order.)
Therefore, the "ang" after "maganda" in the predicate-subject form is not related to "maganda", but is the "the" in "THE woman" (ANG babae).
"MagandaNG babae" = "BabaeNG maganda" = Beautiful woman
"Maganda ANG babae" = "ANG babae ay maganda" = The woman is beautiful
"Maganda ang ngiti mo" is just the predicate-subject order (hence, no "ay") of "Ang ngiti mo ay maganda". Stated either way would sound perfectly normal (not at all poetic) to us since we'd understand them both to mean "Your smile is beautiful".
RE: "Ang babae ang maganda" would mean "The beautiful one is the woman"
It may be understood that way, but in that order, it's really "The woman is the beautiful one".
"Ang babae ang maganda" is OK and will be understood as "The woman is the beautiful one". Although if we are to strictly follow the grammar rule, that should be "Ang babae AY ang maganda" to give it a subject-predicate form.
The "ay" is another linker used to connect the subject to the predicate. However, since "ang babae" and "ang maganda (one)" are both definite nouns in that sentence/phrase, we can do away with the "ay" and in effect understand that like the phrase "the woman, the beautiful one" in English. It's just that in Filipino, we would still consider it as the complete sentence - The woman is the beautiful one. That's because a Filipino sentence does not always need a verb in its predicate, as when the predicate is only an adjective. (That's what FilipinoChatAdmin was referring to in his response).
For example:
Q: Sino ang maganda, ang babae o ang lalaki? = Who is beautiful, the girl or the boy?
A: Ang babae (ay) ang maganda = The girl is the beautiful one - This answer would be considered correct even if we omit the "ay".
"Ang babae (ay) ang maganda" = The woman is the beautiful one
"Ang maganda (ay) ang babae" = The beautiful one is the woman.
RE: Also wondering if maganda ang is ever acceptable in order to make the noun it is describing definite. That's basically what my last question is.
No, "maganda" is just an adjective. The "ang" (the) normally makes a noun definite, while "(ang) isang" (a) usually makes a noun indefinite.
"ANG magandang babae ay naglalakad sa tabi ko" = THE beautiful woman is walking beside me.
"ANG ISANG magandang babae ay kadalasan maraming manliligaw" = A beautiful woman usually has many suitors.
"Gusto ni John na ISANG magandang babae ang maging asawa niya" = John would like A beautiful woman to be his wife.