For a detailed record of all changes since you left (we don't know when that was), read Release/all. The single biggest update was 2013-07-30.
Battle sprites are an interesting new feature, if you use their skills. If you don't want to use their skills, then they're basically a free bonus (perk), kind of like a free trinket slot with a wide variety of trinkets to put in it.
Compared to a few years ago, recipes are generally easier to get now (because of the Hall of Heroes). Crafting costs are lower (because sometimes you have extra Orbs of Alchemy). Playing costs are lower (because there is no elevator energy fee). But heating your items is much harder. Read the wiki article about the Forge, Heat, etc. The real bottleneck is getting enough Radiant Fire Crystals to heat your 5-star items. As a rule of thumb:
* Don't upgrade a 4-star weapon to 5 stars until you have enough Radiants to heat it to heat level 7 or so.
* Don't heat armor or shield, unless you have extra Radiants that you don't need for weapons immediately.
Opening the core is not a huge deal. It's basically one new mission with a new appearance. There might be more missions coming, but don't go crazy about this aspect of the game yet.
Yes, you should jump back in if you ever liked this game. It's still great fun with adorable art. Welcome back.