Is it permissible to sit with a girl to get to know her before the engagement, in the presence of her family, and is this better or is it sufficient to rely on Salatul-Istikhara (the prayer for guidance)?

If you are still attached to the girl, and she is religious and of good character, there is no impediment to proposing to her again. The lack of ease in the first Istikhara does not prevent this; rather, seek guidance from Allah again and propose. As for seeing the fiancée and speaking with her, there is no harm in it, provided a Mahram (definition) is present and it is done to the extent of need.