While many Epserantists are Muslim, I’ve personally experienced a dearth of Islamic material in Esperanto of varying quality and officiality. I can only attest to what I’ve heard other Muslims say and what certain texts say. Given that the majority of Muslims are non-Arab, and that two of the largest Muslim majority nations for Esperanto (Iran and Indonesia) are not Arabophone, debates about Arabic’s use in Islam play into translation into Esperanto, as well as the term's practical usage.
As you’ve stated, it’s expected that a religious term in language A may simply be loaned into language B, even if a perfectly suitable term for it exists. People sometimes go out of their way to do so, but there is a scale from words whose significance is ubiquitous enough to not require a loanword or neologism to words with a specific enough cultural significance that a loanword or neologism is generally uncontested.
As in English, while some may use Allāh in lieu of God, and the apparent Alaho is sometimes used in Esperanto, many Muslims simply use the analogous term for God, or Dio in Esperanto. Proper names unique to Islam are borrowed, although not necessarily directly from Arabic (Muḥammad is Mahometo by Zamenhof, probably from the French Mahomet; Hijrah is Heĝiro, probably from the French hégire or Latin hegiro; mosque is moskeo also probably from the French mosquée).
Regarding words that are generally loaned instead of translated, often their full significance does not completely match up with the extant Esperanto word. A Sūrah or surao in Esperanto, is not necessarily a chapter (faṣl being the Arabic term for a chapter), but one in a set of intertextually dependant “pieces” if you will. Salah is not quite “prayer” in the sense of petitioning a higher power (which would be duʿāʾ), but a ritual more like meditation, and only one kind of preĝo vis-à-vis duʿāʾ. Similarly, Translating Hijrah as pilgrimo or pilgrimado is rather imprecise, as it is not the only pilgrimage in the Islamic vocabulary (ex. Hajj, Umrah, Ziyarah).
When transcribing for a loan: b, d, f, h, k, l, m, n, p, r, s, t, and z are unchanged; hamzah (ء) and ayn (ع) are not transcribed; j is ĵ or ĝ; kh is ĥ, and ḥ is either h or ĥ; dh is z or d; sh is ŝ; ṣ was s, ḍ was d, ṭ was t, ẓ was z; gh is g; q is k, w is usually v in onset, and ŭ in coda; y is j. Tāʼ marbūṭah (ة) is inconsistently transcribed as t (zakāh is zakato), or not transcribed (Shīʿah is Ŝijaismo). Long and short a are both a; long and short i are sometimes distinguished as i and e respectively, or both kept as i; long and short u are sometimes distinguished as u and o respectively, or both kept as u.
That being said, Islamic terminology in Esperanto, unlike other fields, is not a very formalized set of terminology, and usages vary widely between documents and users, with competing translations, loans, and calques being used. Italo Chiussi's word choices for his "Nobla Korano" are somewhat idiosyncratic and somewhat an element of Ahmadi translation standards. Wikipedia can be equally idiosyncratic, and Islamic terminology in dictionaries like Revo can be sparse. So when writing more in detail about Islam in Esperanto, the word choice can be rather up to the user's discretion.
While Arabic is the dominant language in terms of Islamic history and liturgy, Persian and Turkish also hold lexical sway (ex. derviŝo "dervish," from Persian through Turkish), although Esperanto material rarely covers the subject matter in which those two languages are prominent (particularly mysticism). Even within Arabic, different geographic regions refer to the same or similar concepts with different vocabulary. Arabian and Asian muslims call a religious school a madrasa and a mystic lodge a tekke, while North Africans have called both a zawiya. A religious master or saint depending on the region may be called shaykh, hazrat, baba, bibi, lalla, syed, sidi, etc.
The practical linguistic and geography variety of peripheral Islamic terminology adds an additional element to consider when speaking or writing about Islam in Esperanto.