The question about enclitics has been addressed elsewhere on this site; e.g. in C. M. Weimer's answer to Are there exceptions to the Latin stress rules? and my answer to Were enclitics considered part of a word for stress purposes?. (My answer to that second question is not very good; it would be nice if somebody could post a better one.) The correct general rule is debated, but in the specific case of words like animusque, there is agreement that the accent would fall on the heavy syllable immediately preceding -que.
The question about circumeo is different, but hard to answer. As mentioned in the answers to the linked posts above, there were exceptions to the Latin stress rule. Even in cases where the rule applies regularly, it can be difficult to determine the relevant boundaries for the application of the rule. C. M. Weimer's answer explains that even though forms like benefacit may be found written without spacing, the forms of benefacio are thought to have been stressed the same way as the verb facio; i.e. beneˈfacit and not *beˈnefacit.
The issue of the pronunciation of -um
Here is some background information about another issue of Latin pronunciation that is relevant. When a word ending in -um comes before a word that starts with a vowel, the two-word sequence typically scans as if the -um were absent. This, along with some statements from Latin grammarians about the pronunciation of word-final M, has been interpreted as implying that word-final -um (or any other word-final vowel + m sequence) was pronounced not as a vowel followed by the consonant sound [m], but as a nasal vowel sound, which changed according to its environment in the following ways:
before another vowel, a nasal vowel was usually elided. I say "usually" because it seems likely that hiatus was possible. As far as I can gather, in the case of hiatus, the first vowel would apparently scan as short. There is more information about elision in general in the following article: "Elision and Hiatus in Latin Prose and Verse", by E. H. Sturtevant. I will look to see if there are examples of the word circum having the um elided in verse.
before a plosive or nasal consonant, a nasal vowel was converted into a sequence of short vowel + a nasal consonant homorganic to the following consonant. E.g. circ[uŋ] capita.
before other kinds of consonants, a nasal vowel would remain as a nasal vowel, which scanned as a long vowel. E.g. circ[ũː] familias.
Circumeo is an unusual circum- word
Andras Cser's "Aspects of the Phonology and
Morphology of Classical Latin" (2016) has a section on circum- (220.127.116.11.). Like Draconis, Cser notes that the spelling of circum- does not change before consonants.
But in circumeo, circum- is not followed by a consonant. In fact, in this word we can find the alternative form circu-, as in circuit. Cser says the following about the distribution of circum- and circu- in this word:
With ire there is an interesting imbalance between circum- vs. circu-: if the stem form begins with [i], the form circu- is more frequent, when the stem form begins with [e], circum- is more usual (thus circu-it but circum-eunt rather than vice versa, though all variants occur).
Cser says that, although in most words circum- behaves more like the first element of a compound than like a prefix,
circuire suggests prefixation rather than a compound boundary, and hence deletion of the placeless nasal just as is coire
Cser also says that it is uncertain whether the forms spelled with <um> followed by a vowel, such as circumeunt, were pronounced with a consonant sound [m]. Cser doesn't seem to discuss stress, but I assume that that would likewise be somewhat uncertain.
Other Circum- words
Here are the details of what Cser says about other circum- words:
Words prefixed with circum- are much more like compounds than words
prefixed with con-: their meanings are usually more compositional, stem vowel
weakening is hardly ever found in them (circumcidere ‘cut around’ and
circumcludere ‘enclose’ were probably lexicalised early), and circum- can precede other prefixes (e.g. circumobruere ‘wrap around’ with ob-). In this respect circum resembles the other disyllables retro ‘backwards’, intro ‘in’, extra ‘out’, which formed compounds (if at all), but did not function as prefixes in the strict sense of the word.
As I said, Cser doesn't address the topic of stress in this section, so I'm not sure whether compound words starting with circum- would be expected to be stressed any differently from prefixed words.
Here is a link to a relevant discussion on the "Latin Discussion" forum: Composite words