why would i be playing them a second time?
Because they're awesome and you won't get all the skits and endings on your first time through the game (I think you actually can in Totori if you strictly adhere to a guide which is not very fun, but Meruru for sure has things that don't even unlock until NG+ and IIRC Rorona's endings are also such that you'll have to play the game 1.5 times minimum). Also you probably won't have time to make very many powerful items and equipment on your first game, either, just enough to get by but not to tackle the challenging optional/sidequest bosses. The series is good about making NG+ feel empowering, too, what with money and equipment carryover (varies slightly by game).
So, regarding the true end and melvia's end, am I fucked if I killed
before completing melvia's flag?
I think he will respawn? Maybe not, been a while since I finished platinuming Totori... If he doesn't, then you might be...
Picked up Atelier Totori, taking some time with it. How important is keeping track of days? I'm trying to be a little sensitive about using days, but I'm not sure if that's the best way of going about stuff, since I think I'm under-leveled. Those hawk-things at the third area are totally kicking my ass.
Keeping track of days is important but you have several years of game time so don't fret too much about it. At the 3 year mark if you have cleared some requirements (story-related spoilers), you will get another 2 years of game time. Generally, you will want to maximize time spent fighting and synthing and minimize time spent traveling. It's not advisable to avoid battles--these games aren't that grindy but with how stats work in the game (stat/level gaps between you and the enemy are very powerful both in and against your favor) you will have a bad time if you avoid enemies too often. As a general rule of thumb, try not to let either your adventurer level or alchemy level lag behind the other.
Really want to like the game, it's... not entirely clicking yet. I feel like some of that is just some stuff going over my head, though. How does synthesis work, exactly? There's a couple quests that are asking me for stuff I haven't made before and I'm not entirely sure how you're supposed to make it, or figure out the relevant ingredients.
All synthesis recipes are learned from books. As a general rule, raising your alchemy level will not teach you new recipes. You can get books in different ways. Some you can buy, some you can find from exploring, some will be given to you after meeting certain requirements (like getting to certain level). If you're seeing requests for items you can't make yet, just ignore them for now.
Unlike some games where you can "stumble" upon recipes by experimentation in crafting, in Atelier that only happens in the narrative, not in the gameplay. If you don't have the recipe book you will not be able to make the item.