The beracha acharona of Al HaEtz, the Me’ein Shalosh[1] for fruit of the seven species for which Eretz Yisrael is praised (olives, dates, grapes, figs, and pomegranates), is an interesting hybrid. On the one hand, it is similar to Birkat HaMazon in terms of content. On the other hand, it is a single beracha, similar to Borei Nefashot, albeit in long beracha form.[2] Yet, it begins and ends with a beracha form and is of a higher level (see below).
With this background, let us answer your first question. One who ate both fruit of the seven species and other fruit should recite only Al HaEtz to fulfill all the obligations.[3] Since Al HaEtz thanks HaShem “for the tree and the fruit of the tree” generally, this stronger beracha can cover “lesser fruit” as well. In fact, the Mishna Berura[4] rules that even if one mistakenly recites Al HaEtz after eating only ordinary fruit, he still exempts himself from Borei Nefashot. However, since this exemption is based on the language of Al HaEtz, it does not apply to fruit that does not grow on a tree, i.e., produce whose beracha is Borei Pri Ha’Adama.[5] Other sources indicate that even “fruit of the ground” is included in “tenuvat hasadeh”[6] and is exempted by Al HaEtz.[7] The logic is stronger for those who conclude Al HaEtz with the words “al hapeirot,” as opposed to “al pri ha’eitz,” as the former refers to fruit generically and not exclusively to fruit of the tree.
Regarding the order of the berachot acharonot, it is conceptually proper to recite the Me’ein Shalosh first because it is a higher level beracha than Borei Nefashot for one or more of the following reasons: According to some authorities,[8] Me’ein Shalosh is actually a Torah-level obligation; it is longer and more extensive than Borei Nefashot; and it is more specific.[9] However, some poskim say that because of the opinions that Me’ein Shalosh fulfills the obligation for all sorts of fruit (including fruit of the ground), it is preferable for one to say Borei Nefashot first, as it will otherwise be unclear whether he should recite Borei Nefashot afterward. If the Borei Nefashot is needed also for eating something that does not grow from the ground (e.g., meat, water, and, according to many, fruit juice, which loses its status of fruit regarding berachot[10]), this is not an issue,[11] and it would be preferable to recite the Me’ein Shalosh first.
Nevertheless, the accepted ruling and practice for Ashkenazim is to not be concerned with the opinion that one should say Borei Nefashot first, even in cases in which a fruit that does not grow on a tree was eaten.[12] For Sephardim, it is difficult to say. The Shulchan Aruch seems to maintain that “HaAdama fruits” cannot be included in Me’ein Shalosh. Rav Ben Tzion Abba Shaul[13] employs additional strong logic: One who plans to say Borei Nefashot after Me’ein Shalosh is considered like one who has in mind not to have the Al HaEtz cover the Borei Nefashot fruit, in which case there are ample sources that indicate it is not effective for those foods. (One would do well to have this in mind explicitly.) On the other hand, the Kaf HaChayim[14] says it is better to avoid the situation by reciting Borei Nefashot first, although if one did say Al HaEtz first, he would still recite Borei Nefashot.[15] Rav Ovadia Yosef,[16] basing himself on the rule he champions to avoid doubtful berachot even when the Shulchan Aruch approves of them, goes further. He rules that if one already said a Me’ein Shalosh, he should not make a Borei Nefashot. Given his authority, it is hard to tell a Sephardi to not follow his position, at least in regard to l’chatchila situations.