So my question is does my friend have to report his purchase to the IRS after he transfer them to me?
You generally report sales rather than purchases.
Also should I ask my friend to continue keep it on coinbase/GDAX or transfer them to a temporary wallet until my ledger nano s arrive?
The risk of loss is low, but the effort of transferring to your own wallet is lower. Download a Ledger-compatible wallet and transfer the coins. Then, when you get the Ledger, move the coins to the Ledger.