1. In a suit for partition, the preliminary decree will determine the case including if the partition suit is maintainable, if yes, who will get what share and all other issues with regard to rights of inheritance.
After the court passes the preliminary decree, in order to divide the property by the report of a commissioner the court will pass decree and judgement in connection with the allocation of respective share to parties to the suit.
The execution petition is filed to execute the court decree.
2. The final decree is the part of suit, hence can be filed anytime.
3. Execution petition cannot be filed on the basis of preliminary decree alone
4. If the fresh suit is filed for the same cause of action then it may be barred by the operation of law of res judicata, the court will not take it on its file.
You can continue the old case itself as suggested above.