Merkle Tree computations
Option # 2) A node running full-block chain will compute Merkle tree and will send me only the transaction path. Pitfall: the sender will be computing Merkle trees of lots of people. 


This is what happens. You connect to a full node, tell it to send you transactions which match a filter, and then you will receive those transactions along with the merkle tree path.

This is specified in BIP 37 which is used by many SPV wallets. Note that not all wallets use BIP 37 such as Electrum which uses its own protocol and connects to special Electrum servers.


  What reward he is getting for his services?


None. Full nodes are not rewarded for anything unless they are a miner.