the death of a parent I've been struggling to get over since it happened.
This issue is too complex to be settled on a QA site. You should seek help at your school's mental health/counseling center, you can also try independently seeing a therapist.
I started the PhD about 7 months ago, and since then, I feel like I'm not doing anything of use in the group.. Everyone else seems to know exactly what to do
Because they've been there longer than you, and already learned. Hang out with other new students if you want more relatable peers.
they seemingly aren't burdened by any issues of confidence in asking for help, or generally needing direction.
In academia, one of the understated skills is to look like you know what you're doing even when you don't. The majority of successful academics have this skill. It's not hard to learn, and the obvious thing for you is to work on it.
However, if you don't want to go the "hard way" of being candid about your misgivings throughout your career, and you don't like the idea of learning to always put up a front, I would advice reconsidering your career choice. (Note: Reconsider means just that - not "give up now just on that reason alone", but simply give it some more thought to see if it's really what you want.)
I'm not living up to the expectations that he (or my group peers) might have.
You are judging yourself against a bar of what you imagine your advisor and peers might expect. That's not a good idea. Among others: You cannot control their expectations, you are not systematic with this "imagining" and meeting the expectations you imagine may be a waste of your time or even harmful to you.
Instead, you should sit down and come up with some logical goals for yourself. What are you trying to accomplish? Graduate? Become a top scientist? Make your parents proud? Think rationally about what things might be necessary or helpful to reach these goals: Maybe it's keeping your GPA high, or asking at least one question in every talk, or publishing a paper within 2 years, or getting a grant.... Then focus on those objectives, ignore everything else (except to re-evaluate your objectives rationally).
It's hard to chart your own path through life, but that's what being an adult is. The bad news is that it's particularly hard in academia because it's among the most unstructured and freeform professions. But you don't have to do it alone. Some useful resources are: Books about being a PhD student, discussions with your advisor or other mentors you trust, family and friends.
It's particularly good to set objective goals with your advisor. That way, so long as you meet these goals, you know that you're at least not a total failure, and your advisor should certainly be happy. And if you struggle to meet them, you can expect help from the advisor, since he put you up to it. Don't rely on your advisor alone - not all advisors are good in laying out every critical step to success for a PhD student. Of course, you do have to respect your advisor's Way and marry it with your own goals to some extent, since as it would not be very productive to always be pulling in a different direction from your advisor.