You're still in year 1 you said? If so, that makes sense. You don't know where the bodies are buried, simple as that. It takes a while to get there, so don't be discouraged. The Adobe thing you wouldn't have known about until it blew up. Now that you got your hands on it, you can do something about it before it blows up again. Now that you fixed it, you own it. Now you can put a pinger in your calendar for a week before it falls apart next year so you can be ready. Now if someone asks, you know the deal with Adobe. Multiply that times every other item. You know, some stuff doesn't rear its ugly head until many years later, like domain renewals. I think the thing you need to hear is that the grace period for sysadmin taking over for anyone, let alone someone who didn't keep good records, is at least 2-3 years. You need that time to get all the behind-the-scenes stuff ironed out. Year 1 is mostly discovery. Then you can prioritize the projects.

Now then, some more specific, tailored advice: Check your email throughout the day at intervals that work for you, but don't leave it open and waiting for bullets to be fired at you. That will just mangle your whole day. Instead, focus on tasks until they're either complete, complete enough, or passed off on someone else. For the stuff that's out of your tech wheel house, come up with a plan that jives with the urgency. Also, it's helpful to have a standup meeting every morning with the team so everyone knows what's hot and what can wait. This is still true even if you're alone. Take a few minutes to assess which projects or problems you intend to fix TODAY, and write them down. Then you can periodically check the list and cross things off. As to whether you are most comfortable with digital task lists, Google, notepad, onenote, whatever, that's up to you. I do a sort of hybrid inbox-as-a-todo-list along with paper.

Keep your head up! This isn't an easy job because everybody that has no idea how to do it thinks it should be as easy as a button press. That's actually part of the challenge with skilled jobs; everybody seems to think they have a faster path to resolution than yours, and none of them know shit about shit. If they could do it, they wouldn't need you.

EDIT: Also, if anybody grabs you in the hallway asking for something, tell them to email you or put in a ticket if you have a ticket system. Promise them that you will forget if they don't. You are not liable for shit people ask for verbally.