Is it normal to appreciate the bittersweet feeling of loneliness?

It might be important to consider that 'being alone' and 'loneliness' suggest different things.

Loneliness involves being isolated despite wanting social connections, whereas being alone can mean taking time for yourself between social interactions. By exploring where you feel your experience of loneliness fits within these perspectives you can begin to put your feelings into greater context. For example, would you like to connect with others more, and cultivate friendships or do you feel that connection to others is lacking or are you finding some time and space for yourself to recoup, re-energize and/or re-orientate?  

Loneliness, or being with oneself, doesn't necessarily have to be a negative experience. Like you mentioned, there is a peacefulness and tranquillity that you connect with. Is this, perhaps, suggestive of how you feel outside of that peaceful and tranquil space? Do you feel chaotic, hectic, stressed, or disorganized? What is it that the peace and tranquillity bring you that may be contrary to how you feel outside of it? 

Being alone can be giving yourself the time and space to reflect on what is meaningful and important in your life. With this in mind, it's quite reasonable that you are thinking about the future, wondering whether you will become 'a ghost in a shell' after school has ended. You may be giving yourself the opportunity to realize what you want from life and begin to set yourself new objectives. Of course, this is not an easy task, particularly if you are unsure about what you want to do in terms of a 'long-term objective'. Through exploration and careful reflection on this idea, what is meaningful to you and what you would like to experience, you can begin to break down the (possibly daunting) task of setting yourself long-term goals. Writing a journal or keeping a diary can be a great tool to identify and reflect on those ideas over time.

Being alone can be an opportunity to tune in to ourselves, to realize the value of relationships and identify what is meaningful to us. Attuning to these things gives a greater opportunity to live them out as well as express gratitude and appreciation within relationships.