(1) Without time nouns (e.g: 昨天) how can I know these are completed actions?
Chinese language doesn't use tenses like English does, therefore, without "昨天", "我买了书就回家" could mean, "I went home after I had bought the book" or "I will go home after I've bought the book" In both cases, the action "买" is completed (in the past or in the future)
(2) Can I put another 了 at the end of sentence to point out completed actions?
Yes you can -- If you treat the second 了 as an aspect mark, "我买了书就回家了" would indicate both '买书' and '回家' are completed action. However, the 了 at the end of a sentence will be treated as final particle most of the time. The only way to remove the ambiguity is insert 了 between 回家 and write "我买了书就回了家". But having two aspect marker '了' in the same sentence make it awkward to read. Native Chinese would avoid that and rewrite sentence to "我买完书就回了家" , But the best way is to put in time reference "我昨天买了书就回家了" or "我买书之后就回了家" (since you bought book before went home, the first 了 is redundant) to indicate all verbs in the sentence are completed