The tl;dr of this answer is: Why not just use Trickery?
But hey, you asked for a balance check, so you'll get a balance check. You didn't name any of your domain features, so I'll go ahead and label them something pithy. I warn you now, I'm attaching a completely meaningless trademark to all of them.
1st Level - Lucky Strike: An extra 10 points of damage is, on average, how much damage you deal with a 3d6 sneak attack. It's also the amount of extra damage you could deal with a feat like Great Weapon Master, and roughly eyeballing it, taking a -5 and losing advantage on a roll could be called similar enough. In exchange for a limited number of uses, you get to apply your bonus to any attack roll instead of attacks with a limited set of weapons. While nasty at lower levels, this seems balanced... although I foresee problems with this being added to spell damage. You could save yourself a headache by limiting this to weapon attack rolls.
2nd Level - Roll the Dice: Nothing stops a player from always picking 20 for their guess. 5% of the time, they use up a channel and nothing happens. The other 95% of the time, you autodeal 20 points of damage to every bad guy within 30 ft, and take 10 yourself. The closest equivalent is Radiance of the Dawn, which at 2nd level deals an average of 13 points of damage (save for half) to the same group of baddies. I'd say this was unbalanced if it weren't for the fact that, by level 20, Radiance of the Dawn is dealing 31 points on average (even if a bad guy makes their save, 15), while your cleric is still dealing a flat 20, and taking 10 points of damage themselves to do it. I'm therefore going to say It's balanced, but lose the guessing mechanic. If you want this more randomized, I'd recommend having the cleric and the DM each roll a d20 and compare the results. For added fun, the cleric's d20 could be the damage they deal, and the DM's could be the damage taken by the cleric.
6th Level - Hit Me: You are effectively giving bad guys your 1st level ability. Remember how I said that losing advantage and a -5 were similar penalties? Same goes for gaining disadvantage and that -5. This is woefully underpowered, especially considering that other domains can force disadvantage on attack rolls without the bonus damage at 1st level (hi, Warding Flare). Based on the imagery called up by my label and your ability, I'd suggest doing something closer to the opposite- grant an enemy advantage on their attack roll, but you take less damage if it hits. Half damage is on par with similar abilities, such as Uncanny Dodge, though the advantage part still makes it weak. Maybe regain a use of Lucky Strike when you use this class feature?
But, ah, we're looking at balance, not workshopping. Moving on.
8th Level - Potent Spellcasting: I'm calling this what it is, and it pops up for other domains at 8th level. Can't get much more balanced than this.
17th Level - Stack the Deck: ...No. Just, no. At no point is getting the opportunity, for free, to use a legendary, probably should've been an artifact-level item, balanced. Given that you've tacked on a "first bad card doesn't count" clause, This is horribly unbalanced.
That said, maybe there's something that can be done with this ability that is closer to a capstone feature. If I were the sort to make recommendations (and I obviously am), I'd use the Fates card as inspiration and make a class feature that worked similarly to Portent- effectively, you would get to "first bad card doesn't count" someone's roll. Anytime someone makes a d20 roll you don't like, you use this ability and make them roll again. Obviously, something like that would be useable more than once a month, but we're getting sidetracked.
Bottom line, your Luck Domain, except for the last feature, is unbalanced, but useable. the 17th level feature will quickly break any game it's allowed in.
Have you thought about just using the Trickery domain instead?