About setting up failover routing using host zones managed by Route53 in a different account

We are using name resolution in an environment where VPCs built on multiple accounts are connected by TransitGW.
The accounts are configured as follows
All VPCs built in all accounts are connected by TransitGW.

Account A: Account whose host zone is registered with Route53
Account B: Subdomain is registered to Account A to get the primary IP (secondary IP in case of failover) of the server in Account C
Account C: Environment with two servers running

In the above case, the following procedure is assumed

Create a host zone on Route53 for account A
Create Route53 health check using CloudWatch alarm in account C
Add a subdomain as an A record to the host zone created on Route53 in account A.
At this time, associate the Route53 health check created in the C account.

Check if the name can be resolved by nslookup etc. from account B.
If you try to implement the above method, we have the following questions.
(1) Is it necessary to create an inbound endpoint for the Route53 resolver on the C account?
(2) Can the Route53 health check created in account C be used for Route53 in account A?
If so, how should it be configured?

Thank you in advance.