In the vast majority of cases, a "phrasal verb" consists of a very common "base" verb coupled with one or more prepositions/adverbs. Thus, for example, if we take the base verb to look,...
look into (investigate)
look up to (respect)
look down on (disparage)
look out (heed)
look for (search)
look after (protect)
look back (reminisce)
look sharp (hasten)
etc., etc.
As is often the case, the single-word alternatives are significantly less common than the base element in the phrasal verb versions. Sometimes (look sharp, for example) the phrasal verb is undoubtedly informal, but this isn't always (or even, I suspect, usually) the case.
Non native speakers might well think it's even more difficult to learn all the different combinations above than it would be to learn the single-word forms. But from the native speaker's perspective phrasal verbs usually seem easier, because the "building blocks" are so common and familiar.
The net effect of this is that even when a phrasal verb isn't inherently informal, it often seems more appropriate in formal contexts to use a less common single-word form. Apart from anything else, it gives the impression you have a wider vocabulary, since most people would say the highlighted elements in my list are at most "sub-definitions" of the single word look (coupled with various prepositions/adverbs that are so common they barely even count as "words" in the context of an extensive vocabulary).
Since the principles of "formal" English are primarily inculcated within the academic context, where a wide vocabulary is usually seen as highly desirable, students are encouraged (by teachers) and naturally motivated (for their own advancement) to acquire and demonstrate that wide vocabulary.
I hope this explains why phrasal verbs are less common in formal contexts than one might otherwise have expected. It's purely a personal opinion, but I think there's a long-standing general tendency for real (i.e. - informal spoken) English to create more and more phrasal verbs. In total, the language manages to "say more with less" (by using less words, with more significant ways of joining them together).
My advice to learners would be to favour, rather than avoid phrasal verbs, but just be a bit careful with those which are considered "informal", or even "slang". That's what most native speakers do anyway, and I assume most learners aspire to speak like a native, rather than write like a professor (whose prose style might seem awkward/stilted/opaque even to many native speakers).
TL;DR: Use a phrasal verb wherever you know one that means what you want to convey (unless you know it's inappropriate because it's too informal for the context). You'll sound more like a native speaker.
The gerund refers to the act or process of doing something - the activity itself and nothing further.
The -ion form of a root can mean the act of doing something, but usually leans toward meaning its result, effect, or manifestation - something that persists or evidences after the activity.
Why don't some verbs have "-tion" nouns?
This may be a better question for https://english.stackexchange.com, but briefly looking into it, -ion comes from Latin and is generally used with words of Latin origin. Non-Latin words - such as those that are part of the Germanic "core" of English (e.g. all the irregular verbs) won't work with -ion.
Best Answer
In the senses that you give above, we use pull over more often to indicate a brief pause while travelling: to look at a map, to let others pass in front, in response to a police car's red light, etc. We can also pull over without stopping, while to park implies stopping.
We use park more often to indicate a longer stop at a destination.
We can say Let's park and have a look at the map with the basic meaning of stopping clear, but it would be more common to use pull over in that utterance.