[SalesForce] How to get missing Buttons “Reply”, “Reply All”, “Forward” on Emails at the Activity Tab in Lightning Experience

The first things I check when I don't see the quick-actions I expect to see are

1. do I have the permissions to make the change?
2. for create-record actions, is the record type specified on the quick-action one that is assigned to my profile?

It doesn't seem as if the second applies here. But if you are working in a sandbox and you have Email Deliverability set to None or System emails only, then the Email quick-action will disappear from the page. This is true even if you switch Email Deliverability back to All Emails! In other words, switching off deliverability removes the Email quick-action from your layout and you'll have to add it back manually.

About the lack of the Change Status action, I can't think of anything.

Please refer to this: https://help.salesforce.com/articleView?id=actions_in_lex.htm&type=0

In Lightning Experience, actions display in the Global Actions menu in the header, on related lists, on list view items, and in several places on a record page. Where they appear on a record page depends on the action’s type.

[...] The page-level action menu in the record’s highlights panel (1) contains: [...] Global and object-specific quick actions, except for those related to creating tasks, creating events, and logging calls. [...]

The Activity tab (2) contains Create a Record quick actions that point to the Event and Task objects. It also contains Log A Call actions and Send Email actions.

It's a built-in Lightning page behaviour. If you have a Quick Action that creates an Activity or sends an E-mail, it winds up in that tab instead of the button area. They just don't give you any choice in the matter.