1. I don't think the passport photo page needs to be certified. But if you want to do it for peace of mind, you're looking for "Document Certification", and it's £12.75.
2. As long as your most recent payslip and the most recent bank statement is dated within 28 days of when you/your partner clicks to submit the online application, you're fine. Your employer letter must also be within 28 days of when you click to submit the application. Do you have that, yet?
3. I'm not completely familiar with the new application process, but those are the two forms that require filling in. The applicant will also need to take the biometrics form with them to have scanned when they go to give fingerprints, but that doesn't require filling in.