Yeah, it covers his whole body, including the back. I don't think it spans the entire length of his tail, though. It's slightly disjointed in front of him, but not by much -- not enough to matter, anyway.
Fair has 15 frames of landing lag (iirc), so if you land with it in front of a shielding opponent, you're going to get grabbed. You can try to spotdodge and hope that they're slow on reacting, but there's nothing you can do if they shielded you and you're within their grab range.
The lesson is: don't fair a shielding opponent. Even crossover fairs can be dangerous because they can buffer a turnaround grab, but you have more of a chance of catching them with a utilt during their grab's startup lag.
Pika's approach options are limited, so you need to bait before you attempt an fair -- that, or use it to punish a mistake/lag on their part. If they're predicting it and shielding, you need to set it up better.