Are modern fighter jets bulletproof and armored?
With very select exceptions like the Su-34, and the A-10 if you consider it modern, they are not. Even in these cases only the pilot and a few critical parts are armored. Most of the aircraft's skin offers no meaningful resistance even to small arms.

Extensive armor coverage that could withstand modern air-to-air or surface-to-air weapons simply isn't viable for a fighter for weight reasons. Redundancy is used to resist near misses and light hits instead.

The reasons are different depending on the weapon. MANPADS like the Stinger go for the nearest heat source (engine exhaust). Their capabilities against a fighter are limited to fringe cases (flying too low, caught on landing/takeoff, and a very lucky shot), and armoring the engine nozzle isn't viable anyway.

The lightest effective anti-aircraft weapon, the Sidewinder, uses a continuous rod warhead, a ring of steel expanding at almost 1 km/s. Due to high inertia, it will cut through anything except for the engine, major bulkheads and longerons, and hard elements like the A-10's "titanium bathtub". Aramid lining, which is the only thing a modern fighter could afford weight-wise for full-airframe protection, will be cut.

The heaviest is the S-400 SAM, which intercepts the target at 2 km/s with a 180 kg fragmentation warhead. The resulting hypervelocity impact (3+ km/s) has solids behave like liquids, with impact results determined by mass rather than strength. The low odds of surviving a warhead this size aside, when it's mass that determines these odds, it's always better invested in something functional rather than just armor. 

Most mid-size AAM and SAM also fly an intercept course at high velocity and use high-brisance explosives for blast fragmentation. Against resulting high impact velocities, mass is better invested in more redundant hardware, not armor. That is very different from low velocities, common on the ground, where thin layers of high-strength materials can prevent projectile penetration. 

Larger fighters are indeed more resistant to damage than smaller lighter ones (see the one-wing F-15). Armoring a few critical elements can help improve survivability, but this armor has to be very localized. The Su-27 family has an armor plate between the engines, so that one wouldn't damage the other if it disintegrates after a hit. Close air support (CAS) aircraft that attack tanks and other ground vehicles carry some protection for the pilot - notoriously vulnerable to punctures, unlike most of the plane - against ground fire.

A combination of these factors is why armor has largely become limited to CAS aircraft: high-strength armor is very weight-effective against the low velocities of land warfare weapons, but much less so against hypervelocity impactors and fragments used in air combat.

See a related question for a few more bits of info on aircraft armor and protection:
Why do modern fighter jets use 20mm guns?