Hi and welcome!
Fees, first:
Application fee is £1523
Immigration Health Surcharge is £1200
Priority is £573
These fees will all be paid in USD, though, at the stated rate when you apply (it is updated a few times a year, and I'm not sure what the current prices are).
Documents:
The applicant letter is optional and if used, it's usually just to provide a table of contents, or to explain any issues in the application (legal issues, prior immigration issues, etc.). If your application is straightforward, there is no need for an applicant letter.
The sponsor letter is required. In it, the sponsor outlines how they are eligible to sponsor the application (British national, employed permanently making £xx,xxx, etc.) , and a brief summary of the relationship and how you keep in touch.
If you/the sponsor own the home, there is no need for a letter. You just provide the Land Registry document showing you as owner and the most recent mortgage statement. If someone else owns the home, the owner will need to write a letter saying the appkicant and sponsor have permission to live in the house, and you will still need the Land Registry document and mortgage statement if available.
Mortgage statements are typically sent out as an annual summary document, so it's expected to be months old. It's fine. Only the most recent payslip, bank statement, and employer letter have to be within 28 days of the application date.
The employer letter needs to be from someone who has authority to write the letter and can confirm your employment details. Some get theirs from HR, some from owners, ... it really depends on the size/structure of the company. My husband got his letters from the office manager (highest ranked person at the local office) of his old job, and HR from his new job.
For your message history, you've been together since August, yes? So that's 1-2 messages per week for almost a year... that's probably a reasonable amount.
For photos, you only want a maximum of two (I sent one because my husband and I both avoid cameras, so one was all we had). Only you and your partner in the photo(s), usually one from early in the relationship and one more recent one. Take out all the other photos. These are just to show UKVI that you have actually met in person at least once.
Now, for the link... the old link was visa4uk (yes, a government official thought a '4' in the link was reassuringly official-looking, apparently).
https://www.visa4uk.fco.gov.ukHowever late last summer, they started switching everything to online applications, and I'm not sure of the details of the new site. As far as I can tell, you are in the right spot. It is a UK government link, at any rate.
I think I might have missed some questions, but just ask again if you still have questions.