Classic X-bar theory takes all syntactic structure to be binary branching, a controversial assumption. Data like that produced in the question demonstrate why it is a controversial assumption. The example sentences cannot be anaylized convincingly in terms of strict binarity of branching.
But if one is striving to maintain strict binarity of branching, then the structural analysis of the first example sentence might be something like the following:
[Peter [painted [Mary seated]]].
A small-clause-like structure is present (https://en.wikipedia.org/wiki/Small_clause). The words Mary and seated form a constituent, an XP. There is going to some sort vP-type shell structure present in order to accommodate the fact that Mary and seated form a constituent.
The question is good insofar as it reveals one of the central problems with the classic X-bar schema. There is little empirical evidence backing the assumption that Mary and seated should form a constituent. Constituency tests reveal, rather, that the structure is flat: Mary is a constituent and seated is a constituent, but the two together do not form a constituent.
Topicalization does not identify the two together as a constituent:
*...and Mary seated, Peter painted.
Clefting does not identify the two together as a constituent:
*It was Mary seated that Peter painted.
Pseudoclefting does not identify the two together as a constituent:
*What Peter painted was Mary seated.
Proform substitution does not identify the two together as a constituent:
*Peter painted like that. (like that = Mary seated)
Answer fragments do not identify the two together as a constituent:
Who did Peter paint? --*Mary seated.
Conclusion: the two words together do not form a constituent. The X-bar analysis, which imposes strict binarity of branching on all syntactic structure, cannot be correct. The X-bar schema is simply wrong. While some may defend the X-bar schema against this conclusion, I think many established linguists would agree with the conclusion. Note in this regard that the importance of X-bar theory resides with its role in the development of syntactic theory. Few linguists take it seriously these days. Similar structures to the examples in the question are discussed in the article on raising: https://en.wikipedia.org/wiki/Raising_%28linguistics%29.
Some of the lesser questions can be answered much more directly.
seated is the first example is an adjunct, but a particular type of adjunct, namely one that functions as a predication over the object. Such adjuncts are sometimes called participant-oriented adjuncts, since they function as predications over one of the participants, i.e. over one of the arguments. We know that such expressions are adjuncts because they can be dropped from the sentence entirely, e.g. Peter painted Mary.
sentado in the second example is also a participant-oriented adjunct, but this time it is functioning as a predication over the subject. We know that it is adjunct because it too can be dropped from the sentence entirely with little change in meaning: Peter painted Mary. The same is true of the third example.
The fourth example contains both types of participant-oriented adjuncts, one a predication over the subject and the other a predication over the object, as stated in the question. In my view, there is no good way to produce an X-bar analysis of such cases. In fact attempting to do so would be difficult, although it is undoubtedly possible.
While these comments may not be quite what the question is looking for, I hope that they help reveal the problems with the X-bar schema in general. My preferred analysis of such examples assumes a relatively flat structure in which the distinction between arguments and adjuncts is encoded in terms of distinct types of dependencies, as opposed to in terms of varying positions in a prescribed structure schema.
