The influencing style that the BA is using is inspiring. Inspiring is a style that appeals to the emotions and values of the stakeholders, and motivates them to achieve a shared vision or goal. The BA is using an inspiring style by showing them a video case study of a contract renewals team at another company that successfully adopted Sales Cloud, which shortened its time to close and increased its close rate by 30%. This helps to create a positive and aspirational image of what Sales Cloud can do for them, and encourages them to overcome their resistance and embrace the change. References:
https://trailhead.salesforce.com/en/content/learn/modules/business-analysis-stakeholder-management/influence-s

Explanation
When a business analyst uncovers a workflow which could have an impact on another team, they should review the effort and impacts with that team, and work to align requirements across the teams. This is because ignoring or minimizing the impact on another team could lead to missed requirements, conflicting solutions, reduced quality, increased costs, or decreased customer satisfaction. The business analyst should collaborate with both teams to understand their needs, expectations, dependencies, and constraints, and find ways to balance them in order to deliver value for both teams. References:
https://trailhead.salesforce.com/content/learn/modules/salesforce-business-analyst-certification-prep/collaboratio

The user story should include a quantifiable reason why the feature is needed. This helps to define the value or benefit that the user expects from the feature, and provides a basis for prioritizing, testing, and accepting the user story. A quantifiable reason should be specific, measurable, achievable, realistic, and time-bound. For example, "As a service agent I want Salesforce Macros to complete repetitive tasks faster so that I can reduce my average case resolution time by 10%." The other options are either irrelevant or incorrect. Option A does not improve the user story, but rather makes it vaguer and ambiguous. Option B does not improve the user story, but rather changes the user role and perspective. References:
https://trailhead.salesforce.com/en/content/learn/modules/business-analysis-user-stories/write-user-stories

A functional requirement specification is a statement that describes what a product or service must do or provide to meet user needs or business objectives. It should be clear, concise, testable, and measurable. The option B is an example of a functional requirement specification because it describes what the portal should do (allow for partners to upload monthly sales reports) without specifying how it should do it or why it should do it. References:
https://trailhead.salesforce.com/content/learn/modules/salesforce-business-analyst-certification-prep/requirement

Email Proof is the User access and sharing feature that would be used for the following use case: it is the first time a user logs in and they need to be sent an email with a way to authenticate their email. Email Proof is a security feature that requires users to verify their email address when they log in for the first time or change their email address. 2 FA, Single Sign-On, and Login Link are not User access and sharing features that would be used for this use case. References: https://help.salesforce.com/s/articleView?id=sf.
security_email_proof.htm&type=5