Hello there,
First, I'm so sorry for the loss of your mom. Second, my MIL just passed the one year anniversary of the death of her husband of 35 years just last month. I can tell you where she is right now, although everyone grieves differently. At one year, her closet is still full of his clothing. Personal toiletries are gone, but I would say that she still has 60% of his stuff still in the house. Just the other day she was commenting that it's probably time to begin going through it all.
She still has her rough moments, especially lately because it was the 1 year anniversary. The large picture board that we created for his funeral is still in her bedroom; she's just now considering breaking it down because looking at all the photos and memories is starting to get to be too much for her right now.
She has a great group of friends her age and two cousins her age and they have proved to be wonderful support for her and she has become busy, busy, busy doing things with them. This has been wonderful for her. Because although her two sons and our families all live close by, we all work full-time and with kids in school, our lives can be hectic. We all see her weekly, though.
One thing that has been very, very difficult for her to adjust to is what she perceives as a change in her place in this world. She's no longer part of a couple, she's no longer a wife. She's no longer "needed" as she was when my FIL was alive because he required special health care for decades. That change in her "status" for lack of a better word, has been very, very hard on her. She and my FIL were the "hub" of our family and that has now changed. She relies on us much more now and looks to her sons to make some decisions for her. She has confided in me that evenings are the worst for her. Days might be filled w/ grandchildrens' visits, errands, etc. but nights are now empty, unless she's out with friends.
I commend you and your sister for wanting to know what your dad is going through and how he's managing. I imagine he may find it difficult to express the emotions he's experiencing right now, esp. being a man. I would lay off the dating suggestions; I can't imagine after 30 plus years of a happy marriage that he's in a place where he's ready for that at just 7 months later. At one year later for my MIL, that is the absolutely last thing on her mind. Since your dad is in his 50s, he's really still young and he'll be ready when he's ready. He doesn't need anyone pushing him in that regard. I think it is fine, however, to suggest that you'd be willing to help him go through your mom's items, but I really wouldn't push that too much, either. Make the offer, see what he says. But like I said, we're all different and we all grieve at different paces and in different ways. My MIL joined a grief group for awhile and some of the women there were still grieving 7 years after their husband's death! My MIL was flabbergasted at that. She stayed w/ the group for a few more months, but quit after awhile because she DOES want to move forward and not keep holding on as these women seemed to be. I thought that sounded like a healthy decision.
Good luck and again, very sorry for you and your family.