I can't be particularly helpful on the loss of your partner, having never gone through that. Your father, though...my mother died when I was 22. The most useful advice I've got:
1) People say absolutely moronic things, but most often mean well by them. It doesn't make it right, it doesn't mean that what they say isn't infuriating/hurtful/whatever negative reaction it triggers. But keeping in mind that they almost certainly meant well, and made the mistake out of ignorance and not malice, can keep you from lashing out at them over it.
I'm sure, decades from now when some of those people lose a parent of their own, they would be utterly horrified to be reminded of what they said to me. And knowing that made it a lot easier to just let go of my reaction to them.
2) As a corollary, your grief is one of the most acute (if your partner's parents or siblings are alive, they could easily be up there with you), but it's not the only one. Your friends and family are grieving to some extent as well -- some for your partner, and some for the loss of their expectations of what your life would be with your partner. It makes it easier to cut people close to you some slack when you recognize that part of them is reeling too.
3) Grief is not a packaged, schedule deal. There are not 5 discrete phases of coping that everyone progresses through, and the idea that it's linear is laughable. The pop psychologists who popularized and perpetuate this idea of Denial, Anger, Bargaining, Depression, Acceptance deserve to be slapped on a daily basis. Some people rebound amazingly quickly; others take a lot longer to come to terms with things. Some people find immersing themselves in a social environment helps them not to brood; other people need the quiet and introspection that time alone brings. You will grieve in your own way. Right now, judge yourself solely on whether you are functioning on the most basic level. If you are managing to go to work, doing your job, bathing, and eating, consider that a success. If after six months to a year you're still in that barely functioning state -- not able to enjoy time with friends, still depressed easily, not feeling like anything other than the bare minimum is worth the effort -- then you should seriously look into talking to someone trained at helping you through this sort of thing. But if you don't want to do so before then, then don't. Do what works for you, not what other people want you to.
When my mother died, I found I needed concrete things to do on a daily basis; that helped me remind myself that I could still get things done, and life wasn't completely and totally overwhelming. It also let me stop thinking about my loss for a while, while I tackled taking things down to the storage unit or going grocery shopping or whatever. She died in the summer after I finished college; in September that year I started grad work. And I threw myself into it, because that's what I needed. Leaning what I needed to know for my classes, reading papers to develop research questions, troubleshooting lab methods...those were all things I knew how to do, and knew what steps to take, and I think that in and of itself helped me get back to a good place mentally. But, that's me. What you need is something only you are qualified to determine.