I'm sorry to hear about your father. Even though you may have been estranged, I'm sure you had some good times. One way to remember your father is to remember those good times. If you weren't allowed to attend the service, later on, you might leave some flowers on his grave.
Do you have family members who you can talk to ? You might want to get together with those members and have your own memorial in his memory. It doesn't have to be anything fancy. It could be just coffee and cake with your family.
You need to give yourself time to grieve. You may even want to consider talking to a therapist about your relationship with your father. It's something you can do later on that will help you heal.
As far as exercise, you don't have to do a lot to start. Why not start with a daily walk ? Walking is not only great cardiovascular exercise, it's a great way to reduce stress. I do a lot of my best thinking when I'm out walking. Walking helps to clear my mind. So, try taking a daily walk. Do you have a gym membership ? If so, why not go and take one of your favorite classes. There's nothing like a good aerobics class for a pick me up.