Raising money for a startup is in and of itself a full time job in most cases. Seed funding is easy but once you need to get out there and network, it will be time consuming. You can hire a PR team to do this for you.
Consider asking your family for help. If you are married, ask your partner to do tasks they can manage to help you out with time. You can also seek members outside of your home to help if they have free time.
Funding a startup will take a lot of time. Like mentioned, consider asking friends and family I would also consider taking someone or a few people on as partners. Sign and agreement and have them work with your to even out the time investments.
If you can invest 2 whole days, do that. If not, try to work a way to have 2 to 3 hours a day where you can devote to your plans. It will take you longer but it will be worth it in the long run.
I am not sure you will be able to. I think you need at least 30 hours minimum for something like this to really work. You are already working full time with a family. Can you handle working another job?