Почему suite читается ка [swi:t], а suitcase как ['su:tkeIs]?

В первом случае после t e, а во втором после t c.

Потому что слово suite сохранило французское звучание. Родственное русское слово - сюита. Произносится похоже 🙂

потому что во втором нет буквы е

Потому что suitcase произошло от suit ['su:t] - костюм, а не от suite. "е" на конце замечаете? - Это РАЗНЫЕ слова.

1. Это влияние французского языка. Там иные правила чтения
2.Существуют ранние заимствования (они уже ассимилированы в анг/яз) и поздние (самые "капризные") => достаточно часто образуются такие пары.

suite 1670s, "train of followers or attendants," from Fr. suite, from O.Fr. suite "act of following, attendance" (see suit). The meanings "set of instrumental compositions" (1680s), "connected set of rooms" (1716), and "set of furniture" (1805) were borrowed from French or re-spelled from suit on the French model.

suit (n.) c.1300, "attendance at court, the company attending," also their livery or uniform, via Anglo-Fr. siwte, from O.Fr. suitte "attendance, act of following," from Gallo-Romance *sequita, fem. of *sequitus, from L. secutus, pp. of sequi "to attend, follow" (see sequel). Meaning "application to a court for justice, lawsuit" is first recorded early 15c. Meaning "set of clothes to be worn together" is attested from early 15c., from notion of the livery or uniform of court attendants (a sense recorded from late 13c.). As a derisive term for "businessman," it dates from 1979. Meaning "set of playing cards bearing the same symbol" is first attested 1520s, also from the notion of livery. Hence, to follow suit (1670s), which is from card playing.