You can't lookupcan look up things on the Internet during a match per MTR 2.12:
Electronic devices are permitted, but players may not use them to access information that contains substantial strategic advice or information about an opponent’s deck.
When using electronic devices, you have to follow these rules:
Device use during a match other than brief personal calls must be visible to all players. Players wishing to view information privately on electronic devices during matches must request permission from a judge.
There are additional rules for limited tournaments:
At Competitive and Professional Rules Enforcement Level during drafting and deck construction, players may not use electronic devices capable of taking and storing notes, communicating with other people, or accessing the internet.
And as always, the Head Judge always has the final word:
The Head Judge or Tournament Organizer of a tournament may further restrict or forbid the use of electronic devices during matches.
This wasn't always true. Prior to the 2021 MTR update, the wording in 2.12 was:
At Competitive and Professional Rules Enforcement Level during drafting, deck construction, and playing of matches, players may not use electronic devices capable of taking and storing notes, communicating with other people, or accessing the internet (with the exception of taking brief personal calls with the opponent’s permission).
As for the Torrential Gearhulk. I've asked a judge at a Standard PPTQ Tournament (Competetive REL) if it's enough to name a card by describing it as "Blue Gearhulk". His answer was that it's OK, because there is exactly one card that can be described as "Blue Gearhulk" in the sets permitted in the format we are playing. This is per MTR 3.6:
A card is considered named in game when a player has provided a description (which may include the name or partial name) that could only apply to one card. Any player or judge realizing a description is still ambiguous must seek further clarification.
MTR 3.6 also clarifies that:
Players have the right to request access to the official wording of a card they can describe. That request will be honored if logistically possible.
So yes, you can ask about the card.