I would assume so. The blood does not come from your ovaries, it comes from the lining of the uterus. Plus, even with one ovary you could still reproduce.
Yes, you should still have a period every month. If you only have one ovary, instead of your ovaries taking turns every month, the one remaining ovary will release an egg every month. As long as your remaining one is okay, you should have normal reproductive health, chances of pregnancy, etc.
Yes many people if they have some complications get one ovary removed. You will get your normal periods that is every month if your cycles were previously regular You have to absolutely not worry about it. You can also become preganant and deliver a baby. So be assured and nothing to worry.
AS long as there are no other medical complications surrounding the removal of the ovary, yes, you should still have a period every other month. Many women with only one ovary still ovulate and can still have children.
Yes you will, your period is a result of changes in your hormones that is caused as a result in you not becoming pregnant. Not based on how many ovaries you have or do not have. When you do not get pregnant you will have a reduction in progestrone in your system.