Can I re-employ a Ukrainian citizen, who previously worked based on a declaration of entrustment of work and visa-free scheme? His visa-free regime and the declaration ended on 20th March, and the contract was accordingly terminated on 20th March.

...  Now, after the break, can I re-employ this foreigner using the declaration that expired on 20th March, which validity is extended by law and the same time the foreigner applies for a temporary residence and work permit by post?

YES, there are no legal obstacles to re-employ such a person. Under the provisions introduced by the Act of 31/03/2020, there has been an automatic extension of the permitted period of work based on a declaration on entrusting work to a foreigner. Additionally, the regulations launched on 18.04.2020 make it possible to prolong the legal stay for foreigners staying in Poland based on the visa-free regime until the 30th day following the date of cancellation of an epidemic emergency or epidemic state (the one that will be last in force). Thus, if they have worked for you so far based on the declaration, they may continue to work legally.