Is it forbidden to conceal personal matters from one's sister, especially if the sister searches the phone and monitors due to her suspicions, and invokes and curses her sister when the latter tries to prevent her from doing so, knowing that the monitoring sister suffers from depression?

There is no harm in locking the phone and setting a private password for it. The sister does not have the right to open it without permission, because the default assumption for a Muslim is innocence, and harboring ill thoughts about them is forbidden. The sister's supplication will not be answered because it is not rightfully made, and this is one of the impediments to the acceptance of supplications. It is advisable to be patient with the sister and gentle with her, especially since she is suffering from depression, and to strive to reassure her and avoid anything that might cause suspicion. Both of them should endeavor to get married and seek help from female relatives or friends.