For daily quests prioritize the "Chance" one to get R Gacha tickets. Eventually you'll be able to accept 2 daily quests at once, but it's not super important to rush for that since the other daily quest rewards aren't fantastic. I believe you unlock the extra quest slot from finishing stage 4 or 5 of exploration.

About Kurito, R Gacha tickets are the best thing to trade to Kurito imho since they very often give SR Wild 3, very good for SED progression. The R Gacha trade also has a decent chance at netting you the limited N or R girl. As far as getting the SR goes, I wouldn't get my hopes up for it on anything less than a gold button, and even then you may need to try several times. She's really not kind to new players trying to get the SR who don't have a lot of items to trade.

Events>Exploration, there's really no need to rush exploration, there's plenty of cards you can get from the N Gacha that you can feed your wilds into, and honestly levelling up the gacha cards first is better. If you have a girl at 100 and find her again in exploration you get 300-1500 pero depending on her rarity. If you have a girl at 100 and find her again in gacha you get a Wild equivalent to her rarity, which is a much better value. The exploration and gacha cards are different, so focus on levelling the gacha ones first, participating in events, and eventually you'll get all the exploration girls.

Your extra questions:
1) I don't think so
2 and 3) Nutaku occasionally does a "revival gacha" that let's you get a chance at getting old cards by using "revival gacha tickets," I believe the last time they did this they let players vote for what girls were in the revival gacha
4) N-Gachas are exactly what you should be buying with pero gold, personally I don't buy anything else with pero

Another tip from me would be to remember that Moe cards get really good SED gains per level within their early levels, and get practically none past level 80. Sexy cards get most of their SED per level past 80, and Babes always get ~1% of their total SED per level. Personally, I level all my Moes to ~60, then I check this forums Wiki and sort all the cards by maximum SED and just work my way down the list.

Also just FYI, you don't actually need to kill the bosses in exploration, you can actually leave the fight, never kill the boss, and just keep rolling in the exploration screen, so you can farm as long as you want.

Hope this helps