Réussir (à) un examen: using the preposition with this substantive is acceptable but stands as an exception (because technically the person attending the exam is not the person doing the examination; rather it is the person achieving a favourable result at the exam) to standard usage nowadays. It just showcases the usage with this verb, moving away from intransitive or indirect constructions in favour of the direct object complement with nouns (réussir un examen). So you would not want to use réussir à because réussir + direct object noun is simply very typical since the 19th century, and infinitely more so that with the preposition at this point in time. LBU14 (Le bon usage, Grevisse et Goosse, 14e, éd. Duculot, §907, 287 a 8, 774 e 3, 1123 b 3) considers the following examples wouldn't even work anymore nowadays:
En général, elle réussissait À tout ce qu'elle entreprenait (STENDHAL,
Chartr., VI). — Vous avez mille fois plus d'esprit qu'il n'en faut
pour réussir À ce projet (BALZAC, cit. Trésor).
It also refers to another example from the TLFi which wouldn't work and which confuses Châteaubriand with Voltaire's:
The verb uses the preposition à to introduce the infinitive verb, but no longer to introduce the complement, except with examen and the like; the TLFi entry doesn't contain any information about this detail. Yet the standard usage is transitive:
Typically with the inanimate, the verb is intransitive:
Finally, for the sake of completeness, réussir à ce que + conjugated verb (standing together for something like the equivalent of à [pronoun] (faire) + the infinitive verb) is possible but undocumented and is seemingly understood by analogy with the réussir à qqch construction (LBU): « Il pouvait [...] réussir À CE Qu'elle lui permit de la voir quelquefois » (Proust, Recherche, in the LBU14 §1123).
Considering all of this I would therefore use:
La compilation a réussi | échoué / est réussie | un échec.
compilateur n'a pas réussi à compiler.
Il y a eu une erreur lors de la compilation.
Le compilateur n'a pas réussi la compilation. [based on the quelqu'un réussit quelque chose prototype]
Q2. Using the preposition à with something else than with an examen-related substantive or for introducing an infinitive verb, is not standard today. Nevertheless, using it is not impossible/necessarily incorrect. That being said, usually when there is an inanimate subject, the verb is intransitive. Saying that the compiler succeeded at compiling is a complicated way of saying the compiling was a success because what else than compiling does a compiler do? So alternative ways of expressing this have been provided.