You can negate the continuous spell card's initial activation with cards like Solemn Judgment or Magic Jammer.
Once successfully activated though, you can't use 'spell card activation' negation effects like the above, even if the continuous spell has a subsequent activated effect, like the trigger of Black Whirlwind, or Royal Oppression's Quick Effect. That's because the spell card's activation was when you first played it to the field, what you are doing after is 'activating an effect' of an already resolved card. However effect negation can be chained to it, you could use Stardust Dragon against Royal Oppression (as long as Royal Oppression is destroying a card on the field - usually it does not, but it would if it was being used against Summon Priest).
Lastly, cards like Spell Canceller, and Imperial Order (forbidden in Advanced format) will 'switch off' any continuous cards, and negate any of their activated effects too.
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The following cards are all Continuous Trap cards that have some form of negation, just like "Imperial Order":Royal DecreeThe Emperor's HolidayTyrant's TiradeRoyal CommandRoyal OppressionRare MetalmorphSeal of WickednessTalisman of Spell Sealing"Talisman of Spell Sealing" is the most similar to "Imperial Order" considering it can negate Spells as well.
No, it can never do that. It has an Ignition Effect (spell speed 1) and can only target face-up cards. So that means it can't do anything to those cards while they are face-down, and when they do activate, Alector can't chain his effect to them. Basically his effect is used against active Continuous Spell cards, as well as Field Spells and Equip Spells.
No monster can chain to a Counter Trap in order to negate the activation. Quick monster effects are spell speed 2, and only Counter Traps can chain to Counter Traps, spell speed 3. So cards like Light and Darkness Dragon and Stardust Dragon can't be used against them. Some monsters can prevent the activation of Counter Traps such as Jinzo. A few others have continuous effects that negate all trap effects. Sky Scourge Invicil is one, when summoned with a Dark monster as tribute.
You can activate Quickplay Spell cards in your opponent's turn, if you have Set them on the field. As well as that, some of your face-up continuous and continuous-like cards may have a trigger than activates when a certain condition is met, these can activate in the opponent's turn too (Black Garden is one).
There is only one way to negate his effect and that is by using a effect negation card the moment it is summoned as jinzo's effect is spell speed 2 your cards effect will work first.