Most likely your score did not drop because you closed an old card, but because this reduced your available credit (and increased debt to credit ratio). Closed accounts in good standing remain on your report and count towards the FICO score for about 10 years. You can bring the score back up to your maximum possible by pre-paying all your credit cards to $0 before their statement closing dates.
But it also gives 3% cash back for the first year and 2.5% after that on everything, so if you spend more than $11800 per year on “everything else” (besides Amazon, gasoline, groceries), it’ll be better than Citi DoubleCash. You can also make up for the annual fee by using the card to pay for things you normally wouldn’t because of fees, like income taxes.
No. You can churn the miles cards just for the signup bonuses and to accumulate miles, but otherwise the cards are not worth it. Besides, all the good ones have annual fees. Dollar for dollar, the mile rewards are rarely worth more than 2% cash back unless you redeem for first class or business, but dollar for dollar you are still spending more to be fancy.
In case you didn’t see it, we have a thread for Best Reward / Cash Back Credit Cards.