Here are the sentences with the relative pronouns or adverbs that can be omitted crossed out:
The TV which I bought last week broke down 10 minutes ago.
I am reading the book that my sister gave me.
The man whose bag was stolen in the shopping centre yesterday came to the police.
Jeff knows someone who can help you.
The boy whom I am talking to is my cousin.
Note: "whose" cannot be omitted as it shows possession, and in the last sentence, "whom" can be replaced with "who" in more informal contexts, but it cannot be omitted altogether. However, in casual speech, it is often replaced with "that" or omitted, leading to the formal structure of "who I am talking to."