There's a version that «пока» as a farewell phrase originated from something like «while we are away, be OK» or a phrase like that.
[ Whilst ] may persevere in the English lexicon, even if only due to status as a diminished vocabulary advocacy term of contention.
Whilst ‧ 1776 ‧ Abigail Adams ‧ wlh.law.stanford.edu/wp-content/uploads/2011/01/cunnea-timeline.pdf ‧
Whilst ‧ 1789 ‧ Washington inaugural ‧ www.archives.gov/exhibits/american_originals/inaugtxt.html
Whilst ‧ 1845 ‧ quotecatalog.com/quote/james-k-polk-i-cannot-whils-baVXO37/ ‧ www.reddit.com/r/quotes/.../i_cannot_whilst_president_of_the_united_states/ ‧ quotefancy.com/.../James-K-Polk-I-cannot-whilst-President-of-the-United-State ‧
Whilst ‧ 1877 ‧ supreme.justia.com/cases/federal/us/95/149/
Whilst ‧ 1903 ‧ www.law.cornell.edu/supremecourt/text/195/27
Whilst ‧ 1940 ‧ en.wikiquote.org/wiki/W._C._Fields
Whilst ‧ 1999 ‧ www.ncbi.nlm.nih.gov/pubmed/11281882
Whilst ‧ 2018 ‧ gettysburgian.com/2018/11/opinion-stop-using-whilst/
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The connection seems clear enough: https://en.wiktionary.org/wiki/%D0%BF%D0%BE%D0%BA%D0%B0#Adverb
It's loosely comparable to how English speakers may part with a very informal "Later," shortened from "See you later."
Yes. It's a complex sentence with two clauses. Each clause has a different subject-predicate pair (брат работает, я готовлю), so it's basically two sentences stacked into one. Russian almost always requires a comma between clauses (in rarer cases, a colon, semicolon, or a dash might be used). If a clause is embedded inside another clause, we would put commas before and after it.
Present (both verbs, «рабо́тает» and «гото́влю»).
The past tense would be «Мой бра́т рабо́тал, пока я гото́вила» (if «я» is a girl), or «Мой бра́т рабо́тал, пока́ я гото́вил» (if «я» is a boy).
My brother reads = мой брат чита́ет, while this sentence has рабо́тает = works.