Is it permissible to supplicate for marriage to a specific person, while writing general phrases on social media that might be understood as referring to them?

There is no harm in supplicating to Allah to marry you to a specific person, as long as it is permissible. However, writing phrases that express your love for him opens the door to temptation. It is permissible for you to ask one of your mahrams to propose marriage to him on your behalf. If he then proposes to you, that is good and excellent. Otherwise, you must stop thinking about him and ask Allah for a righteous husband.