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As I understand the first lookup request is sent to the node which is the closest one in the routing table to the info hash of the torrent
During the process of peer lookup I can receive many nodes. When I perform next peer lookup can I start peer lookup from one of them or I must start from the peers in my routing table?
The details of the Kademlia routing and replacement algorithm can be found in the original paper. Basically, you only replace nodes in your routing table when they start failing; however you subdivide the bucket around your ID until the smallest bucket has less than K nodes (where K is as specified in the bittorrent DHT protocol documentation). When starting searches, you use the K routing table nodes in your routing table bucket containing the routing ID of the key being searched.