First answer here, let’s see how this goes.

Now it’s important we keep in mind that our sources for the Inka are actually quite limited - beyond a number of colonial-era accounts written by the Spanish or Latinised indigenous elites, we’re mostly left with the archeological record. Therefore we don’t necessarily know in detail what the Inka thought about the past (their understanding of which was different from ours anyway).

However, we can definitely infer it!

First off, did the Inka draw cultural/political legitimacy from past empires in the area? Yes. It’s not the Wari in this case, but instead the large Tiwanaku empire) which existed at the same time as the Wari, but further south and whose wealth came from sophisticated agricultural exploitation of the Titacaca basin (plus some good ol’ conquest tribute). The Tiwanaku civilisation established a large ceremonial city (called Tiwanaku) located near Lake Titicaca, filled with elaborate-cut stonework and monumental architecture. Even after its collapse the city remained an important site for pilgrimage and ceremony in the Andes, and the Inkas integrated it into one of their foundation myths as a mythical homeland; in this story the nearby lake was where the ✨sun, moon stars and humans ✨ (plus the Inka founder Manco Capac) ere created; humans and Manco then travelled underground all over the earth. This myth therefore both explained why the Inka came from Cusco and not Tititcaca while enabling them to claim the glorious legacy of Tiwanaku for themselves. It’s also believed that an Inka story about petrified giants is inspired by stone monoliths at Tiwanaku, while one of their carvings of the sun might be a precusor to the Inka sun gods. All this clearly shows the Inka saw the Tiwanaku as some kind of antecedent.

Now, the Wari. Interestingly, there doesn’t seem to be the same kind of ritualised attempt to portray the Wari as precursors on the part of the Inka, even though the Wari were actually quite a bit more influential on the Inka than the Tiwanaku were! Just for starters, it was the Wari who invented the famous Andean quipu (the knotted-string recording system) that the Inka used.

The Wari also came up with mit’a (the system of labour tribute to the state), mitma (forced resettlement of conquered peoples to elsewhere in the empire), a network of collcas (agricultural storage buildings) extensive agricultural terracing and the policy of building large road networks and creating settlements along those networks. All of these developments would become important parts of the Inka empire, and indeed the Wari road system would become integrated into that of the Inka. The Wari administrative centre Pikillacta was actually located close to Cusco, and although it was abandoned by the time of the Inka, in earlier times it certainly had a cultural impact on the Cusco valley, as evidenced by the polychrome Wari pottery found there, while the Inka elite’s woven tunics were possibly descended from Wari textiles. So although we do not know whether the Inka actually saw themselves as successors to the Wari, they were definitely their inheritors.

That said, some have theorised that Wari sites were deliberately captured and turned to cult sites by the Inka (see the article below) so maybe they did see the Wari as their antecedents after all! Welcome to the magic of History Without (many) Documentary Sources™.

I’m not going to try too hard to answer your last question about similarities between the empires because I’m not an expert, but I will say:

1. We don’t fully know because unlike the Inka there are no direct documentary sources for the Wari, so we’re left only with archeology and that’s hard to interpret in terms of political structure.

2. People disagree on what the Wari were like. Some think it was a confederation of states with a common religion, some a militaristic empire that spread by force, and some that it used religion, force and economic innovation to spread. Certainly they used their agricultural prowess to expand at a time other civilisations like the Moche were suffering from drought - this largely took the form of extensive agricultural terracing, although this didn't work out so well for them in desert regions. The Inka, for their part, made deft use of alliances, strategic marriages, reciprocal agreement and finally threats and warfare to expand. They were helped that by the time they reached their only serious rival, the Chimu, they were so big as to crush all opposition. Although agriculture played a role in their expansion, the Inkas were also aided by the invention of freeze-dried potatoes, and were more (relatively speaking, not absolutely) successful at adapting themselves to new environments.

3. The above innovations by the Wari that influenced the Inka show there were a lot of similar features.

4. A comparison of the occupation of the same valley by the Wari and the Inka indicates that in general the Wari acted as a more centralised state that imposed hierarchies on below while the Inka were able to take advantage of the degrees of local bureaucracy & centralisation created by the earlier empire to simply install itself above the existing hierarchy. This pattern was repeated over the Andes, with the Inka making extensive use of local peoples to govern.

Hope this answers your questions!

The paper I mention above about the Wari & Inka Cult Sites: Sillar, Bill, et al. “MY STATE OR YOURS? WARI ‘LABOR CAMPS’ AND THE INKA CULT OF VIRACOCHA AT RAQCHI, CUZCO, PERU.” Latin American Antiquity, vol. 24, no. 1, 2013, pp. 21–46.

Sources:

Schreiber, Katharina J. “Conquest and Consolidation: A Comparison of the Wari and Inka Occupations of a Highland Peruvian Valley.” American Antiquity, vol. 52, no. 2, 1987, pp. 266–284.

Encyclopedia of the Incas, Gary Urton & Adriana Von Hagen, 2015

Handbook to Life in the Inca World, Ananda Cohen Suarez & Jeremy James George, 2011

The Incas (Second Edition), Terence D’Altroy, 2015