Short answer: Basically, "tulis" and "menulis" are the same.
"Tulis" is a base verb, it can be transformed to "menulis" (to write), "ditulis" (is written), "tertulis" (is written) etc.
For daily conversations in informal situation, instead of saying "menulis" (formal), we use just "tulis".
They are the same, they mean "written", as a passive.
The prefix di- means that you took a root-word of a transitive verb, and you turned it into passive.
It's a transitive-passive.
Root-word: beli (to buy).
Membeli: to buy.
It's transitive, because you buy something.
-Ter is the same kind of prefix, but for intransitive verbs.
Source here: https://masteringbahasa.com/indonesian-prefixes
So, applying this logics,
ditulis means "is written" in the transitive meaning, and "tertulis means "is written" in the intransitive meaning.
By transitive/intransitive, here, they mean "action made by an agent"/someone.
It's a bit hard to understand, and doesn't seem to make sense, said like that, but this is an example:
Difference with ‘di-‘
• Pencuri itu ditangkap polisi
(The thief was caught by the police)
• Pencuri itu tertangkap
(The thief was caught)
So, I deduce from this reading, that if you simply want to say "the letter is written", but you don't care who wrote it, or don't focus on it, you could use "Korat itu tertulis".
And if you want to mention the author, you could use "Korat itu ditulis oleh..." (The/that letter has been written by...)
I don't think that this is what transitivity is about. In your example sentences with the thief, "by the police" is a prepositional phrase that tells us some more about how the thief was caught, or rather, by whom. But the sentence can still function without it (becoming the sentence from your second example).
Transitivity is about the verb acting on some further object, not by it. For example:
"I ran" (intransitive; no object)
"I ran the program" (transitive; the program is the object that is being run)
Passive sentences flip the object with the subject to emphasize it, so in both of your sentences the thief is the subject.
I disagree. "Writing" alone doesn't exist in English. Except as "a writing", but here, it's a verb. A writing, as the result of the action of writing would be "penulisan" in Indonesian, and if you mean the continuous present, it would be "sedang tulis" or "sedang menulis".
Here, you can use "Saya tulis buku" they do accept it. "Saya menulis buku" is also accepted. No difference.
This same explanation comes back very often from Indonesian people, I don't know why, for instance, many people say that membaca = reading and baca = read. It's wrong, there's no tense difference between both.
Tulis is the root word. Menulis is the derivated word.
Like baca is the root word, and Membaca the derivated word.
Like makan is the root word, and Memakan the derivated one.
Both Saya makan and Saya memakan are correct, and have same meaning.
Both Saya baca and Saya membaca are correct, and same meaning.
Both Saya tulis and Saya menulis are correct, and with the same meaning. (menulis = men + tulis)
See here for instance, "tulis" is considered as a synonym for "menulis", in the Kamus Besar:
The only difference there is, in my opinion, it's that it's more formal to use the non-root version of the verb, so "menulis" is more formal than "tulis". (there's also probably something related to transitive/intransitive verbs, or something like that)
The subject is always before the verb, like it's the case in English, as long as it's not a question (as it's the case in English).
You confuse the pronoun-subject, and the possessive-pronoun, because they have the same form, but the word order tells you if you have a pronoun-subject or a possessive.
For instance: Saya baca = I read.
Saya is subject.
Kucing saya = my cat.
Saya is the possessive (my).
Because it's placed after a noun, and it determines this noun.
The reason is that you cannot use a singular without a determiner in English.
The no-article is only used with plurals. To express generalities.
Horses like flowers.
All the horses in the world, horses in general, like flowers in general.
The horses like flowers.
A special category of horses that I mention, like flowers in general.
You cannot use "like flower".
If it's a singular, you have to mention "a flower" (any flower) or "the flower" (a particular flower I mention).