Its critical to know about the leader of the company and how she is leading the company. Knowledge of the Digital Marketing and SEO industry. This will by and large help you understand the other employees of the company as they are going to work with you not CEO.
Do they have experience in your industry? Have they served anyone in recent past or currently serving like yours. This will help understand their understanding of your target audience.
Overall Digital Marketing is changing very fast. Blink and you miss. Thats why you should ask questions related to the latest changes or Google core updates, what is trending etc.
Ask them to present a SEO Strategy for you. This will help you understand what they are going to do in next 3 to 6 months.
Ask about the automated mails they send on weekly or daily basis. Weekly, bi monthly and monthly meetings they do. Reporting is necessary and crucial in dealing with a agency.
Know about all their clients and the industry they serve. This will help you understand what you can do.
Screaming Frog, Ahrefs, Semrush and many more tools are their when it comes to SEO. Ask them what are they using. Its crucial.
Blogs or Content goes hand in hand with SEO. Its crucial to know whether they will write the content or it will be written by another agency.