Does the owner of a prepaid call cellular phone (mobile) in the
Ukraine have to pay local
charges for an incoming international call paid by by the initiator of
the call? For example if I was to call from New Zealand "this" cell
phone in the Ukraine will the owner have anything to pay as a result
of me calling
her?

The short answer:
As long as the called party is logged into it's own network, there
will be no costs issued for him/her.

The long one:
Any mobile subscriber has one "home network" (the one to which he/she subscribed).
This network is called HPLMN (Home Public Land Mobile Network). When
he/she receives a call while logged into its HPLMN there are no costs
to pay for him/her (regardless who calls and where from).
If the subscriber is logged into another network it occurs the
so-called "roaming" (=switching from one network to another). This
"foreign" network is called VPLMN (Visited Public Land Mobile
Network). When someone tries to reach the roaming subscriber, the
calling party dials the phone number and it lands into the HPLMN of
the called party; this will forward the call to the VPLMN of the
called party and the call will reach its destination. The call costs
will be splitted as follows:
- the caller party pays the "connection" to the HPLMN of the called party and
- the called party pays for the "connection" from its HPLMN to the roamed VPLMN.

Very short answer: No, there is no fee for incomming call in Ukraine. obo

No, incoming calls is free if you use your cellular phone in the
Ukraine (don't use roaming).

There is a law in Ukraine which prohibits any kind of charges for
incoming call, that's why it's completely free for the owner of the
cell phone to receive you call from New Zealand.

This sim card offers free incoming calls:
https://www.mindlogic.com/SIM_CTRY_ukraine2_DTL.shtml
jd