Just a few problems. The rest is OK.
Sentence 3: should be "gave a lengthy speech". Lengthy not length. Also "prime minister" not "primer minister".
Sentence 4: should be "sigh of relief when he arrived home".
Sentence 6: it's not clear WHO was begging. Was the speaker begging, or was she begging? Most likely the former, in which case the sentence would begin with "After begging me to stop smoking".