Thank you for your question. I am sorry to hear about your situation and pray that allah (swt) grants you peace and happiness.
You have posed three questions:
1. Are our spouses predestined for us?
The topic of predestination is a long discussion in Islamic theology which is outside the scope of this short Q & A website. However, in a nutshell, the school of Ahlul Bayt (as) does not recognise predestination nor complete free-will as correct beliefs. This means that we do not believe all our actions and destinies are out of our hands and that we are incapable of deciding which fate to choose nor do we believe that everything is in our hands and there is not a higher power that has a role to play in our chosen actions. The Ahlul Bayt (as) have taught us that there is a middle path which is that man has the free-will to choose which destiny he would like to follow but with boundaries. There are many things which man has no control over, such as natural laws like gravity. But there are many things he does have control over, such as his own actions and words he chooses.
When we take this approach, we see that choosing a spouse has both these elements. Neither is it completely predestined so that you have no say in it whatsoever, nor is it completely in your own hands. We must strive to make the best decisions within the realm of free-will we have been given and rely on Allah (swt) always.
2. What does Islam say about unmarried females? In the absence of a family
and children, how do we discover the purpose of our destinies?
Islam certainly places a lot of emphasis on marriage and building a strong family structure as a unit of a successful society. However, we must know that our primary purpose of creation is not dependent on being married or not. Our primary purpose of creation is to know Allah and to reach perfection and this is achieved through knowledge, self-purification and submission to Allah (swt). Indeed, marriage is a means to attain this lofty goal and has huge benefits and one must not deliberately ignore this sunnah of the Holy Prophet (saw).
3. Can u share some duas for attaining peace.
Alhamdulillah, we are blessed to have a wealth of duas at our disposal thanks to the Ahlul Bayt (as). Duas can be quite personal and each person will find peace and solace in a different dua, depending on ones mood and state. If you are struggling, may I suggest the 15 whispered prayers attributed to Imam al-Sajjad (as) as a starting point. These can be found towards the end of al-Sahifa al-Sajjadiyya and have been recommended by many teachers of akhlaaq to be recited regularly. As with any dua, simply reading it is not sufficient and will not bring about the desired effect, rather, understanding the words and contemplation is what is required.
May Allah (swt) grant you and your brothers everlasting peace and happiness in the company of the Ahlul Bayt (as) in paradise.