It's up to you whether to accept unconfirmed transactions or not. It is likely they'll be confirmed in short order, but there is still a possibility they might not, so for larger values you may want to wait for one or more confirmation(s)
Verify that funds were paid to an address by supplying the transaction ID, the recipient address, the message used for signing and the signature. For the case with Spend Proof, you don't need to specify the recipient address.