When you mark a field as required in Object Manager, the field is universally required to save a record on that object in the user interface. However, the field is not required to save records via the API on that object, unless you also mark it as required on the page layout.

Bucket column allows you to categorize report data into groups without creating a formula or custom field. You can create buckets for different ranges of values and assign labels to them.

A dependent picklist and a custom picklist are the two features that can be used to fulfill the requirement. A global picklist and a multi-select picklist are not features that can be used to fulfill the requirement.
Here is a more detailed explanation of why A and B are the correct answers:
a) Dependent Picklist
A dependent picklist is a picklist whose values are dependent on the value selected in another picklist. This is useful for ensuring that only valid values are selected for a field. In this case, the administrator can create a dependent picklist for the category field on accounts and cases, with the values for the picklist being dependent on the record type selected. This will ensure that only the relevant picklist values are available for selection based on the record type selected.
For example, the administrator could create a dependent picklist for the category field on accounts and cases with the following values:
Record Type: New Account
Picklist Values: Residential, Commercial
Record Type: Existing Account
Picklist Values: Renewal, Upsell, Cross-sell
This would ensure that only the relevant picklist values are available for selection when creating a new account or an existing account.
b) Custom Picklist
A custom picklist is a picklist that is created by the administrator. This is useful for creating picklists with values that are specific to the organization's needs. In this case, the administrator can create a custom picklist for the category field on accounts and cases, with the values for the picklist being specific to the organization's needs. This will ensure that the picklist values are relevant to the organization and its customers.
For example, the administrator could create a custom picklist for the category field on accounts and cases with the following values:
Picklist Values: Residential, Commercial, Land, Multi-Family
This would ensure that the picklist values are relevant to the organization and its customers.

An external ID is a custom field that has the external ID attribute enabled, which means it can be used as an identifier when importing and updating records from an external system. It allows administrators to match records based on a unique ID value from another system instead of using Salesforce record IDs, which may not be available or consistent across systems. An auto-number field is a custom field that automatically assigns a unique numeric value to each record, but it cannot be used as an identifier when importing and updating records from an external system because it is generated by Salesforce and may not match with the external system's IDs. A rich text field is a custom field that allows users to enter formatted text, images, and links, but it cannot be used as an identifier when importing and updating records from an external system because it is not unique or consistent across systems. A record ID is an internal ID assigned by Salesforce to each record, but it cannot be used as an identifier when importing and updating records from an external system because it may not be available or consistent across systems. Reference: https://help.salesforce.com/s/articleView?id=sf.custom_field_attributes.htm&type=5

To show a component that shows LinkedIn data only to sales users when they are on their mobile phones, the administrator should filter the component visibility with two conditions:
User > Profile > name = sales User, which checks if the user's profile name is "sales User" Form Factor = phone, which checks if the user's device is a phone Filtering with view or role will not achieve the desired result. Reference: https://help.salesforce.com/s/articleView?id=sf.app_builder_page_visibility_rules.htm&type=5