It might not seem like a lot of money today, but those $35 in BTC can one day be worth $135 or $335 that your friend is just wasting for no reason. You wouldn't be doing that with fiat, why do it with a currency far more valuable? I understand that he won't waste the whole amount, but only the required transaction fees, however, there is still the possibility that he makes a mistake and the coins get lost.

Since your friend is a newbie, he might not know much about testnet. All the features from the mainnet can be played around with in a testing environment and you don't have to spend your real coins. Wallet addresses are different and you need to get your hands on some testnet coins, but it's a great learning ground.  

Make sure your transaction is signed otherwise if it is unsigned it could contain your master public key which would let your friend have all your current and future public keys (and addresses). You may not want them to know that for privacy reasons.

Otherwise when the transaction is signed, it is broadcasted to the network and everyone sees it and the transaction will be included in a block and remains there forever; so there is nothing risky about sending a signed transaction to someone else to broadcast although I have to say it makes no sense to do that.

For that purpose, best is to use Electrum on testnet, maybe multiple wallets too, get free funds from testent faucets and learn for free how the things work.
Then there's no risk at all. And if you're nice enough, after the tests you'll send back to the faucet the remaining testnet bitcoins.

So you mean he wants to combine two transactions with your sign raw transaction?

He won't be able to do that what he can do only is to broadcast the transaction. The generated raw transaction is unique for every transaction and private keys are not included in this.

Why don't you just broadcast it instead of giving it to him for safety purposes?

No. Your raw transaction doesn't include your private key. Instead, it includes a digital signature which can be used only for that transaction and becomes invalid if transaction data is changed.
By the way, why doesn't your friend let you broadcast the transaction yourself?

@JasonSato
Hello
With python example and there web link to empty out old private key.
https://bitcointalk.org/index.php?topic=5392986.msg59753846#msg59753846

Which ones and why? Every wallet from bitcoin.org is open-source; if you want to verify the code, then so be it. If you don't want or can't understand it, then you'll have to take everyone's word for it. It doesn't make sense to not trust reputable open-source software. That's bitcoin in the end.

I think JasonSato is talking about these dust amounts, not the puzzle rewards.

If that's the case, most do it to advertise themselves. Stating messages in the blockchain is an expensive way to advertise and I don't think there's a major benefit. Check: https://bitcointalk.org/index.php?topic=5149678.0