Worf raises "shields and deflectors" in "Encounter at Farpoint," with Tasha doing likewise in the same situation in "Hide and Q."
The deflectors can survive atmosphere at high speed for a while; the hull beneath can be heated to 3300 degrees just fine in "Arsenal of Freedom," while comparably a freighter's hull reached the same temperature before disintegrating in "Symbiote." The material of a GCS hull is tritanium ("Where Silence Has Lease"), which is, even in small chunks, too tough for UFP hand weapons to melt.
The Enterprise is also seen studying a flaring unstable yellow star at point blank, which the deflectors are mostly able to cope with. Also can survive a direct full-tubes whack at point blank by a Constellation class. Can deflect solar flares, but it is not recommended that a ship go unshielded through them.
Season 3: Shields may be extended 5 kilometers from the ship in "The Defector."
Season 4: "Brothers" - the Enterprise can generate force fields in its interior.
Navigational Deflectors. As seen in "Outrageous Okona," the navigational deflector functions as a shield of sorts when the ship is stationary. As noted in "Best of Both Worlds," the deflector handles enormous quantities of power. As seen in "The Battle," it moves interstellar hydrogen, dust, gas, etc out of the way while the ship passes, with very little lead time. The precise mechanism of operation is not entirely clear.
Season 5: "The Next Phase" introduces the phase cloak - a device that makes ships completely invulnerable to fire by passing them out of phase. Romulans have been experimenting with it. A variant of this technology is also seen in "Time's Arrow," and the fully functional Federation model of the phase cloak is then seen in "The Pegasus." "New Ground" - deflectors are down 15% after collision with a high energy subspace wave. This suggests an absolute upper limit of 300-8,000,000 yottajoules for the energy normal strength deflectors can take.
Season 6: "A Fistful of Datas" - a 15 second personal force field can be improvised from and powered by a communicator with a few spare primitive electric components, stopping 6 bullets from a handgun. In "Chain of Command," we see a portable purpose-built deflector emitter, a device roughly the size of a tennis ball.
"Hero Worship" - full shields of a GCS use the output of no more than half its fusion reactors and equal to six.
"Relics" - shields at 23% during increasing solar flares (threatening to engulf the ship) will produce shield failure in three hours.
"Suspicions" - new metaphasic shields allow a shuttle to survive immersion in a star.
"Descent" - 10,000 rads of radiation and hull heating to 12,000C come before shields decline to 61%. The Enterprise may adapt its shielding to metaphasic easily. The Borg vessel in "Descent" was destroyed by an artificially induced solar flare.