You are still married to your wife in the eyes of the Church.
Yes. You would need to submit your marriage to the tribunal to determine nullity or validity.
You do not mention the baptismal status of either yourself or your spouse. That does have bearing on the avenues open to you. The Pauline or Petrine privilege may also be available if unbaptized.
You should not be “engaged” to anyone until you are declared free to marry. You might be setting up your fiancee for a terrible dissapointment should your marriage be found valid. You could not marry as long as your spouse is alive.
Only Catholics are bound by the Catholic form of marriage. You were under no obligation to observe this form.
It is a common misunderstanding.
Two non-Catholics marry validly when they exchange vows in a religious or civil ceremony providing there are no divine law impediments (like a previous marriage, close kinship, etc).
This chart may be useful to you: