Considerable part of the answer to the question can be found at the link: https://ukraina.interwencjaprawna.pl/can-a-refugee-who-has-already-received-temporary-protection-in-germany-receive-it-again-but-in-poland-this-is-assuming-that-such-a-refugee-will-thus-give-up-their-protection-in-germany/
Additionally, it is worth indicating that entitlements under the Special-purpose Act are granted provided that the stay of the Ukrainian citizen was registered within 90 days from the date of entry into the territory of the Republic of Poland.
If the registration of the residence of the Ukrainian citizen takes place within 90 days, then there is no impediment to the granting/complementation of the data indicated in the databases and thus the granting of the status “UKR”.
The other issues raised in the questions have not yet been regulated in EU law, thus there is no uniform system to exclude the possibility of duplication of aid/benefits.
The Polish authorities are obliged to comply with current legislation, which clearly states in which situation assistance should be provided to Ukrainian citizens. In this respect, in the case of mandatory benefits, there is no condition of not receiving benefits in another EU country or having a residence status there. The authority may require the submission of documents proving that they have renounced the form of protection they have received in another country or that they have not received benefits under this status, provided that it is investigating the specific case and that the granting of assistance is optional (the authority may or may not grant assistance).
However, it should be borne in mind that in the case of refusal to grant an optional form of assistance, the authority should prepare a justification explaining why this form of assistance will not be granted e.g. due to the use of assistance in another EU Member State, in which case it will be necessary to consider whether e.g. assistance received in another EU State counts towards the income criterion.
From the beneficiary’s perspective, however, it makes sense to forgo benefits in the country in which he or she is not staying, as the Member States are in the process of preparing a system for temporary protection that will include data on the assistance/benefits provided to individuals. This means that, in the future, a person who drew benefits from two sources simultaneously may face negative consequences.