So conversion rates and figures are one of the more difficult things to compute in the Medieval period. The seminal work on this is Richard Bulliett's Conversion to Islam in the Medieval Period. His method, which has been critiqued but little improved upon relies on so-called biographical dictionaries to try to determine when a given proportion of the population converted. By looking at Arab patronymic names, combined with the dictionary's record of dates of death, you can tease out a somewhat representative sample of the population and when it converted, with certain caveats (e.g. the subjects of such dictionaries will inevitably be disproportionately urban and well-off). So for instance you might have a name listed in a dictionary as "Muhammad (d. 800) ibn Muhammad (d. 780) ibn Ahmed (d. 760) ibn Jorge (d. 730)" and then say "aha! either Ahmed or Jorge converted to Islam!" with a rough estimate for when that might have occurred. Add up enough of these and you get a pretty good picture.

The problem is that there just aren't enough biographical dictionaries for Spain. The record in Persia is far better and as a result his conclusions for Persia are far stronger. Unfortunately I don't have a copy in front of me, but if I recall correctly Bulliett's conclusion was that, yes, a majority of the population of Muslim-controlled Spain did eventually convert. The key caveat there being "Muslim-controlled", particularly given that that came to represent a smaller and smaller proportion of the population.

As for how Spanish was preserved? Unfortunately I can only speak in general terms as I'm not an Andalucia expert or a historian of Spanish linguistics (Muslim Spain tends to invite specialization) but it shouldn't be especially surprising the Spanish was preserved. For one thing, as I said, there was pretty much always large portions of the Iberian peninsula that were not under the firm control of Muslims. Moreover, by no means is there a correlation between Islamization and Arabization. Persia was one of the first regions to be conquered and was also experienced truly rapid Islamization based on Bulliett's analysis and yet Persian, not Arabic, remains the everyday language. Arguably the more interesting question might be why Egypt and the Levant found it so easy to give up Greek.

Arabic, in many regions, was variously a liturgical, intellectual or elite language in many regions and the medieval period was quite comfortable with bi-lingualism generally. Again, with the caveat that I'm familiar with the Islamic side of this rather the Spanish, it's my understanding that the Arabs ruling Spain would have been far more comfortable and tolerant of a Spanish-speaking Christian than the re-conquering Spaniards would have been of an Arabic-speaking Muslim, so where where Islamic Spain was comfortably multi-lingual with Arabic and Spanish, the re-conquerors would have been something a bit more "nationalist".

edit: also where I'd love to see some input from a Spanish Medievalist is that Spain presents one of those really interesting cases how do you tell what people really believed and it's my understanding that this is better studied by experts of, say, the inquisition than by an Arabist like myself. But in general terms at the end of the Reconquista there was this paranoia about crypto-Muslims and crypto-Jews among the Moriscos who were forced to convert. On the other side, and less well known is that Bulliett's hypothesis certainly includes the possibility of crypto-Christians who only pretended to convert to Islam to gain the various benefits that came along with that. While in territories that remained firmly Muslim for centuries on end the concerns about this disappear but because Spain was so contested this adds a further wrinkle to the problem of finding out just who exactly converted and when, aside from the basic lack of sources.

Spanish was not preserved. It developed in the peninsula alongside Euskera (a language isolate thought to derive from the pre-Indo-European Aquitanian), various other Romance languages and, for several centuries, local Arabic, Berber and Hebrew dialects.

As I explained [a few days ago] (https://www.reddit.com/r/AskHistorians/comments/43kzsf/what_religion_did_the_common_people_under_islamic/czjbt14), Muslims only came to be the majority in Al-Andalus by the 12th century. Even though the prestige languages of Spain were Latin in the Christian kingdoms and Arabic in the Muslim realms, the common folks on both sides of the border spoke a plethora of Romance dialects (and the Basques spoke Euskera). The Romance dialects of Al-Andalus are usually referred to as the Mozarabic language. It was mainly the language of Christians who lived under Muslim rule but there's also evidence that some Muslims and Jews spoke it as well.

Most of Spain was (re)conquered by Christians by the mid-13th century and the Reconquista was complete in 1492. Now these later centuries lie a bit outside of my field of study. But until an expert comes along, I'll venture an educated guess.

We do know that Muslims continued to be the majority (or a significant minority) in some Christian kingdoms, Aragon and Valencia in particular. We also know they continued to use their Arabic dialects in law, for instance. We also know the reign of Catholic kings signalled the end of the inter-faith tolerance that was characteristic of Spain before them. Jews and Muslims were forced to convert or face expulsion.

We do know that the Jews who were expelled in 1492 carried their language with them. It still survives and is basically a medieval Castilian dialect, known as Ladino.

We also know that Muslims who remained under Christian rule were forced to convert between 1501 and 1525. Their descendants were expelled from Spain in 1609. Well, without claiming much expertise I'd think the use of Andalusi Arabic must have been in decline from the Reconquest to the forced conversion in the 16th century as more and more people would switch to contemporary forms of Portuguese, Castilian Spanish or Catalan. Even if Andalusian Arabic continued to be used in secret after that, the last speakers must have left the peninsula in 1609, bringing with them Castilian loanwords to Morocco and Algeria where they settled.

Fun fact: Christians living under Muslim rule spoke a Romance dialect but mainly used Arabic characters to write things down. (Use of Latin and Hebrew characters is also attested, but was less widespread). A few centuries later some descendants of Muslim converts to Catholicism living under Christian rule continued to use Arabic characters when writing in Castilian Spanish.