Single mothers have the same options as other single people. Whether to get married or not will have to be a choice she makes. Single mothers may find it more difficult to find the right partner, though, because they will be more concerned with identifying a partner who will look after her child. Sometimes, single mothers have difficulty in dating because their priorities and their schedules are influenced more by their children, making it hard to find time to date. Dating for single moms is also beset with its own problems, as decisions must be made about when to introduce a new boyfriend to her kids.
No, it isn't the only option at all. I'm not sure where you got this idea from. There are many single mums in this world who have decided to forgo marriage and focus on raising their children to the best of their ability. They have extra burdens on their shoulders, but to them the strong love for their children trumps everything and they manage to motivate themselves to make the most of the situation.
Single mothers are single because perhaps marriage did not work out for them, or it just did not happen at all. It is an option that perhaps had expired. I agree that in some cultures, single mothers are looked down upon by their own family and friends, but in today's day an age it has been proven that single mothers can do just as well if not better than some married couples in raising their children, thus making marriage not the only option.
I don't think it is the only option. Which is worse - being a single mother or being in an unhappy marriage? And not only is it bad for the husband and wife, but it is also destructive and harmful for the child. I stayed in an unhappy marriage for many years for the sake of my children. I only ended it when something happened that showed me that it was harming them. Studies have shown that it is best for a child to be raised in a happy home, regardless of whether there are one or two parents.