I merged your posts to give the complete story of this relationship and given the problems with the finances, and lack of trust, I don't see this as a healthy relationship, until you have talked, and cleared the air, and defined the bounds of good behavior, between you. From what you have written, there is very little working together, or sharing the responsibility of the relationship.
https://www.askmehelpdesk.com/womens...me-341824.html
You have many areas of this relationship that your questioning and they all take you talking honestly to resolve. Or else all you have are two people playing house, and that looks good on paper, but wont survive in reality.