No, it can't.
His normal summon can't be negated, so Solemn Judgment can't be used there. Also, note Solemn cannot be used against monster effects, so it cannot be used against his activated effects either.
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No, Stardust Dragon's negation effect is a spell speed 2 quick effect, which cannot be chained to a spell speed 3 card such as Solemn Judgment.
Yes. Because you are negating its summon, you are doing it at a time when it is unable to use its own negation effect, and moreover, it cannot chain its Quick Effect to a Counter Trap anyway, so is unable to stop Solemn Judgment being used against other cards.
Jinzo, Royal Decree and Trap Stun negate the effects, Trap Jammer, Solemn Judgment, Seven Tools of the Bandit negate both activation and effect.
Yes. Because Obelisk the Tormentor is only protected from card effects that do not target, Tribe-Infecting Virus will be able to destroy Obelisk the Tormentor via its effect.
Obelisk the Tormentor (Effect Monster) is not Ritual Summoned nor does it require a ritual. To summon Obelisk the Tormentor, you must Tribute 3 monsters (it is treated as a Tribute Summon).