"She does not miss me."
Translation:Io non le manco.
You picked the wrong meaning of "mancare" :P
"Non sono mancato da lei" is the passive form of mancare, which refers to its transitive meaning, "to miss" as the contrary of "to hit": it can still be translated as "I am not missed by her", but it sounds like a roundabout way of saying "she hits me".
"I am not missed by her" as "she doesn't feel my absence" would be "Io non manco a lei" (intransitive meaning of mancare), and that's where "Non le manco" comes from.
Most clitics have more than one function, but in your example you're using its article form: non must stick to the verb and a+le becomes alle, so it should be "non manco alle donne". Le can indeed be feminine plural as clitic pronoun, but not as indirect object, rather as direct object: "non le conosco" (I don't know them) and "non le parlo" (I don't speak to her).
Is it the Italian verb that determine if the clitic pronoun will be direct(accusative) or indirect(dative)?
If the Italian verb is transitive, then I'll use the "direct clitic" - accusative? mi, ci, ti, vi, lo/la, li/le.
If the Italian verb is intransitive, then I'll use the "indirect clitic" - dative? mi, ci, ti, vi, gli/le, loro/gli.
Is it correct? What website could I use to search if a verb is transitive or intransitive?
Unfortunately it's not always that easy, as many verbs can be both, and a transitive verb can have an indirect object as well (e.g. dare in its usual transitive form obviously wants a dative as well). Most dictionaries will tell if a verb is transitive, intransitive or both; unfortunately not all of them clearly state if you can use an indirect object and to what effect: the collins dictionary tends to go by examples, wordreference tends to list them as compound forms. Unfortunately I don't know of any explicit enough.
Speaking from a French background which also has these sorts of verbs, I find it useful to think of "manca" as "it is missing," so "io non le manco" would be "I am missing to her," which is a clunky way in English to say "she misses me" (imagining "I am missing" to mean that I am missing in a physical sense rather than the abstract, just for sentence construction purposes - if I am [physically] missing to her, she does not have me with her: she misses/does not have my physical form, so to speak). Same with "piace" - "it is pleasing."
This is what I was taught - I would be grateful for input.
The word order in Italian is only flexible "in groups": some words, like "non" and clitics, stick to the verb (the auxiliary if composite), and when more than one occurs the order is fixed, i.e. first non, then indirect clitic, then direct clitic. It gets even more complicated when you add the other clitics, e.g. si, ci or ne (there is a nice clitic ordering rule in paragraph 2.3.1 of this PDF). They must go before the verb in most conjugations, and are attached at the end of others.
le is the indirect object. It means the same thing as a lei. Which one you use depends on the position in the sentence. Just before the verb you use le (in that position, it's called a "clitic", which are direct and indirect objects appearing before the verb). When the pronouns appear elsewhere in the sentence, they are called "tonic" or "stressed" pronouns, and have a different form: "a lei".
Look up the tips and notes on clitics in this course. I really can't think of a way you'd use a direct object pronoun except before the verb, because it appears alone. When indirect objects are used, if they're not in front of the verb, they are usually preceded by a preposition, so you know what's going on.
"I give the book to her" = (io) le do il libro or (io) do il libro a lei
Direct object: the book
Indirect Object: her
I was marked wrong for non le manco io
I think that it's because putting io after the verb is an emphatic, and the sentence doesn't indicated that emphasis is required.
Duo does accept io non le manco. I think it might be awkward to say io a lei non manco even though technically correct.