For example, 'look back' is a phrasal verb. And the verbs 'recall' and 'remember' have the same meaning as that phrasal verb. 2. So when can we use 'recall' instead of 'look back'?
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.
Phrasal verbs were often eschewed in expository and formal writing because educators had taught that phrasal verbs were inferior. Although most native speakers of English use phrasal verbs all the time in conversation, many of these speakers will avoid those verbs whenever they adopt a formal writing style.
P.S. I happen to like phrasal verbs. I use them wherever and whenever I can.
A phrasal verb is simply two words that together form a single verb.
As for formality, while it may often be true that phrasal verbs sound a bit more informal than a synonymous verb that is a single word, I don't think that's always the case, for a couple reasons. Sometimes, even in formal settings, the most natural way to say something is by using a phrasal verb. Moreover, some other verbs can be used informally, or as slang, meaning those verbs would sound more informal than a phrasal verb. Therefore, I don't think there's any reason to steer clear of all phrasal verbs in formal writing.
For example, the phrasal verb get up can mean get out of bed after waking up, as in:
I like to get up before 6 o'clock on weekdays, so I can leave the house before rush hour.
If you're trying to avoid get up just because it's a phrasal verb, your available synonyms are slim. One thesaurus I checked offered rise, arise, stir and rouse, but I don't think any of those would be better options, even in a formal document.
A similar example would be make up, which NOAD defines as "be reconciled after a quarrel." The thesaurus offers plenty of examples, but many of them are figurative, or multi-word idioms:
be friends again, bury the hatchet, declare a truce, make peace, forgive and forget, shake hands, reconciled, settle one's differences, mend fences, reconcile
As for an example when a single verb would be more informal than a phrasal one, suppose I told you,
I want to go out driving so I can show off my new car.
I could replace the phrasal verb with the single word floss, but that wouldn't make the sentence more formal. (In fact, it would make the sentence more informal; I could find this definition of floss only in the Urban Dictionary, which specializes in slang.)
I suppose we can often make something sound a little more formal by replacing a phrasal verb with a single verb (for example, I think, "I don't know if I'll ever return to France" may sound a little more formal than, "I don't know if I'll ever go back to France"). Still, that's not always the case; it depends on the verbs in question.
As a footnote, if phrasal verbs were good enough for the eloquent Churchill, they are good enough for me.
English, being the result of a mix of a Germanic substrate and heavy Latin/French influence, often has more than one way to express the same idea.
French doesn't use phrasal verbs much. Take for example these French-derived words:
The original Germanic language has fewer distinct verbs, and prefers using adverbs to alter the meaning:
Latin/French-derived expressions are often considered "fancier" than Germanic ones, perhaps unjustifiably so. There is absolutely nothing wrong with the Germanic expressions, and you should feel free to use them in speech or writing in any register, formal or informal.
Note that not all phrasal verbs correspond to a French/Latin non-phrasal verb, but the pattern occurs frequently enough to serve as an explanation for a perceived difference in formality.
http://homes.chass.utoronto.ca/~cpercy/courses/6361lamont.html#Early%20Modern not only explicates 'phrasal verbs' and their history, but also recommends many helpful books.
Section "VII. Summary" summarises the answer to your 3 questions:
VII. Summary
The Old English ancestors of modern phrasal verbs were generally inseparable-prefix verbs, although some separable forms did exist. The influences of the Norman Conquest and Old Norse on ME eroded Old English OV syntax, and this catalyzed the production of separable adverbial particles and the phrasal verb in Middle English. In Early Modern English, phrasal verbs grew rapidly in dramatic and less formal texts, while new nominal-derivative compounds and rules about pronominal-object placement arose. In Present-Day English, phrasal verbs are identifiable by particle movement (when transitive), stressed particles, incapacity for adverb intervention in the verb phrase, translation, and passivization. Prepositions can be distinguished because they cannot move, they are unstressed, and adverbs can intervene between the verb and the prepositional phrase.
See section "VI. Syntactic Tests for Phrasal Verbs in Present-Day English"; it is too long to reproduce here.
The underlying question concerns phrasal verbs vs Latinate cognates (ie: The etymology of 'look back' is Germanic, but that of 'return' is Latin.) See "V. Phrasal Verbs in Present-Day English, and Regional Variation":
Examples of the first type include “put up with” and “do away with”, which qualify as phrasal verbs because they can be translated by the single Latinate verbs “tolerate” and “abolish”, although their particles are not movable: “I put up with traffic every day”, not *I put with traffic up every day.
Hiltunen explains that phrasal verbs were used extensively in Early Modern English dramatic texts because of their variable shades of meaning and productive capacity “to be expanded to form new idioms” (161). Akimoto notes also that “phrasal verbs occur more frequently in letters and dramas than in essays or academic writing” in the eighteenth and nineteenth centuries (221). This confirms that phrasal verbs occupied a lower social position in Early Modern English than, perhaps, single Latinate verbs that could fill their semantic fields, which gives rise, incidentally, to a syntactic test for phrasal verbs. However, phrasal verbs continued to become entrenched.
