It's using "mixed inflection" because "ihrer" is a possessive determiner/pronoun (third person singular). It is mentioned in the list with the examples "mein, dein, sein, etc). Mixed inflection in the dative form always ends with 'en'. It would have been "eigener" if it were using "strong inflection".
It is weak inflection in eigenen because the determiner ihrer has an ending. Mixed inflection is an unnecessary concept.
I've found the flow chart in this link extremely helpful: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html
@innuli @BastiaanMoto : Mixed inflection is used with possessive determiners. http://en.wikipedia.org/wiki/German_adjectives#Mixed_inflection
Yes, articles and adjectives decline differently, especially when in combination with each other. There are some good links earlier in this thread which should help (plus in other lessons). Here's another: https://yourdailygerman.com/2012/10/08/adjective-declension-german/
This would not be used when someone has died. It would normally be used when someone has a mental condition, dementia etc. where they have lost contact with the world around them. It could also be used if someone was in some sort of trance, under the effects of drugs etc. such that they were not aware of their surroundings but that would depend on the context. It would not normally be said of someone who was daydreaming in my experience, although the symptoms would be much the same for a short while. That is probably because this expression is normally used for somewhat longer term or permanent states.
Possessive adjectives don't have strong, weak, or mixed inflections (partly because nothing comes in front of them; you can't say "a my book" or "that his chair").
They inflect like the indefinite article ein or like kein. (Like the latter, they have plural forms.)
The endings are similar to the strong inflection of adjectives, with the ending being like the last letter or two of the definite article (e.g. in ihrER Welt like in dER Welt) almost all the time.
The main exception is that masculine nominative singular and neuter nominative/accusative singular have no ending at all: ihr Buch, not ihres Buch (like ein Buch rather than eines Buch, despite das Buch with an -s on das).
- Jetzt ist sie in ihrer eigenen Welt.
That's the only other one.
There are only four units in this sentence (Sie - ist - jetzt - in ihrer eigenen Welt), and unlike English, adverbs don't (usually?) go at the end of a sentence, so there's just the default option of "after the verb (and possibly a pronoun object, if there is one)" and the "right at the beginning, before the verb" one.
'She is now in her own world.' Should be accepted, surely.
@RobertHJMa: I already told you one year ago that that translation is accepted.
Please, from now on, take screenshots of your rejected answers so that you can provide evidence for a sentence not being rejected. Do not simply state that '...' Should be accepted, surely. when that sentence is accepted. Such comments achieve nothing.
(After you have taken a screenshot, upload it to a website -- e.g. imgur -- and then insert the URL to the image into your comment.)