Part 1:

First I will address the mixing aspect of this question, and right away I will get down to the meat of it: genetic studies have shown time and again that mixing from Europe in the Philippines to be very little. The largest study seems to be the Genographic 2.0 Next Gen project, which was conducted in part by National Geographic. One of the reference populations was Filipino. The breakdown is as follows: 53% Southeast Asia/Oceania, 36% East Asia, 5% Southern Europe, 3% South Asia, 2% Native American. Of course, these numbers can vary within the archipelago. Some Filipinos will have no admixture from Europe or the Americas, some will have more. But in general we can see here that the archipelago clearly did not experience the kind of intermixing and intermarriage that, say, Mexico did (average Mexican-American is 67% Native American, but features far higher percentages from Europe, as well as Africa and Central Asia). Here is the study in question. Just control+f to look for the populations: https://genographic.nationalgeographic.com/reference-populations-next-gen/

So, then. The question is, why is this the case? Why did the Spanish not "intermingle" more with the indigenous population? From reading William Henry Scott's works on the Philippines at the time of early colonization by the Spanish, we may be able to gain some insight into difficulties that would arise. The Philippines' polities were really based on the sea. Communities were connected, rather than separated, by water; even going from one part of an island to another, using waterways seemed to be the preferred method. There was quite a lot of trade an exchange of both goods and people: a sultanate in Maguindanao was founded by a Melakan prince, Brunei and Maynila were on relatively close terms politically and economically, and Filipinos (it's an anachronistic term, yes, but there really isn't a better one) themselves travelled all over Southeast Asia as merchants or mercenaries, Burma and Timor being examples.

Basically, as the historian Vicente Rafael comments, the societies that were the focal point of Spanish colonization stressed mobility and deemphasized territorial boundaries. The mobile (not nomadic though) and dispersed nature of the polities tended get in the way of the Spanish attempts at colonization and conversion. The Spanish attempted to resettle populations (and appropriated native words such as barangay for this purpose), but this had varying levels of success. Into the mid-18th century, places such as Mindanao, the more inland groups in the rainforests, and the groups in highland northern Luzon were still really not under the authority of Spain.

So immediately we already see a big difference between, say, Mexico, and the Philippine archipelago. Philippine societies were fundamentally different than the Aztec Empire that the Spanish encountered. There were "empires" in the archipelago, but Southeast Asian empires were a bit different. Ultimately they were based around city-states that had a sort of outward projecting influence economically ("mandala states"), but not necessarily through military dominance. For example, the Sultanate of Sulu was by any measure a massive "empire" in terms of area under its influence; but that was just it, influence and alliances. A sultan would technically rule over various datu, but those datu would themselves be the actual leaders of their barangay. Rafael argued that this sort of looseness in structure contributed to difficulties in colonizing the archipelago.

The above combined with the relative lack of interest in the Philippines on the part of the Spanish led to a rather low amount of Spanish people actually living in the archipelago. The resources (as important as they were) that the archipelago was of interest for were not as attractive to potential Spanish settlers as the gold and silver that the New World colonies had. In addition, the actual military presence in the islands was rather small. Generally speaking, the Spanish military presence was limited to places such as Maynila, Cebu, and Zamboanga, important ports and seats of government. These were important ports for international trade, but were utilized mostly in this limited capacity. Within these areas, the Spanish rulers established restrictive residency laws that discouraged settlement outside the walls of Maynila, for example (the walls being those of Intramuros, which was a walled city built in Maynila after it was defeated by the Spanish). Why discourage interactions with the natives? There was a fear of repeating the large scale miscegenation between Indians, Africans, and Spanish in the New World; in fact, no sizeable population of Spanish-speaking criollos ever emerged either. My thinking is that this situation was an attempt to keep a potential educated Spanish-mestizo class from creating problems politically, and this leads naturally to the role of Spanish language education in the Philippines.

Simply put, Spanish language education in the Philippines was limited. The Spanish evangelized and led services in the local vernacular languages. Translation into local vernaculars was in fact a cornerstone of conversion of Filipinos to Christianity over the years. Though violence was a tool, the Spanish in the Philippines preferred to try to use translation and native languages to gain religious followers. It's actually kind of funny that from the late 16th century through the 19th century the official language of the state was Spanish. There had even been mandates to educate the Filipinos in the language. However, this did not end up happening. Schools that were established, such as the Escuela Normal de Maestros in 1863, were opposed by the friar orders, likely because the prospect of indigenous speakers of Spanish would be a threat to their influence. The colonial government was relatively weak, and a true schooling system was never established, thus Spanish was not really spread very effectively. By 1903, only about 1% of Filipinos had received "superior education" and thus were undoubtedly fluent in Spanish (Spanish was the language of higher education in the Philippines).