The best type of sandbox for each team member to use is a developer sandbox. A developer sandbox is a copy of production that includes only the metadata, such as objects, fields, layouts, etc. It does not include any data, such as records or attachments. A developer sandbox is ideal for small projects that do not require data testing, such as developing new features or customizations. A developer sandbox has a storage limit of 200 MB and can be refreshed once per day. A developer sandbox is also cheaper than other types of sandboxes. A full sandbox is a copy of production that includes all the metadata and data. It is ideal for large projects that require data testing, such as performance testing or integration testing. A full sandbox has the same storage limit as production and can be refreshed every 29 days. A full sandbox is also the most expensive type of sandbox. A developer pro sandbox is similar to a developer sandbox, but it has a larger storage limit of 1 GB and can be refreshed every 5 days. It is ideal for projects that require some data testing, such as data migration or quality assurance testing. A partial sandbox is similar to a full sandbox, but it has a smaller storage limit of
5 GB and can be refreshed every 5 days. It is ideal for projects that require selective data testing, such as user acceptance testing or staging testing

The app builder should use a global picklist value set to share the list of values for the Status field across each object. A global picklist value set is a set of values that can be used by multiple picklist fields on different objects. This can ensure data consistency and reduce maintenance efforts. Option A, C, and D are not features that can share picklist values across objects.

* The deployed permission set will merge with the existing permission set in production, meaning changes made in the sandbox will be added to the existing permission set after deployment.References:
* Salesforce Help - Permission Sets

The app builder should use two tools to automate this process:
Process Builder: This is a type of automation tool that can execute actions based on certain criteria. In this case, the process builder can have a criteria that evaluates if an opportunity goes to the closed won stage, and then execute an action that posts a message to a Chatter group.
Workflow: This is another type of automation tool that can execute actions based on certain criteria. In this case, the workflow can have a criteria that evaluates if an opportunity goes to the closed won stage, and then execute an action that posts a message to a Chatter group. Option A and C are not tools that can automate this process.

Data is unable to be deployed with change sets. Change sets are used to deploy metadata components such as custom objects, fields, workflows, reports, etc. from one Salesforce org to another. However, change sets do not include any data or records from the source org. Users will need to use other tools such as Data Loader or Data Import Wizard to migrate data between orgs. [Source]