Exchange 2016 to SE and Exchange Online questions

Hi,

We're currently in the process of migrating from Exchange 2016 to Exchange Subscription Edition (SE), along with moving a portion of our mailboxes to Exchange Online. We have approximately 3,000 mailboxes, and around 2,000 of those will eventually end up in Exchange Online—for various reasons (don’t ask why…).

I have a few questions I'd like to clarify and hope you can assist:

Exchange On-Premises Questions:

1. If a user mailbox is moved to Exchange SE, can they still access shared or user mailboxes that remain on Exchange 2016?
   
   • Do we need to migrate them in the same batch to preserve access/permissions? (should't be an issue in the same Exchange Org right?)
2. If a shared mailbox is migrated to Exchange SE while the user mailbox remains on Exchange 2016, will access still work?
3. Do we need to point the Hardware Load Balancer (HLB) to the new Exchange SE servers before mailbox moves to allow proper client connectivity and proxying back to Exchange 2016?
   
   • Or is it okay to keep the HLB pointed to the Exchange 2016 servers until all migrations are complete and then switch it over? Proxy upwards from Exchange 2016 to Exchange SE?
   • What’s the best practice here? Pros/cons?

Exchange Online Questions:

1. If we want all outbound mail to go through the on-prem Exchange environment—even for Exchange Online mailboxes—is this configured via the Hybrid Configuration Wizard (HCW)?
2. Is the Litigation Hold status preserved when migrating a mailbox to Exchange Online?
3. Can a mailbox hosted in Exchange Online access a shared mailbox still residing on-prem? (Should't be an issue right?)
4. Can an on-prem mailbox access a shared mailbox that has been migrated to Exchange Online?
5. For mailboxes with Full Access or Send As permissions (e.g. user mailboxes tied to shared mailboxes), do they need to be migrated together in the same batch to retain functionality?
   • We’ll be using native Microsoft migration tools (no 3rd-party solutions).
   • If I recall correctly, separate migrations will still allow Full Access?!?, but Send As may not work properly unless migrated together. Is that still accurate?