Are cover letters necessary to add to my initial FLR(M) application? If so, what information should they contain and should both myself and my sponsor write one?
The applicant doesn't need to include a cover letter, unless there's anything complicated to explain (like criminal convictions, previous refused UK visas, documents you cannot provide etc.)
Your sponsor can include a letter, but it's not listed on the required documents for FLR(M), so I don't think it's strictly necessary for FLR(M).
If the sponsor does write one, it should include:
1) How they are eligible to be a sponsor (their UK citizenship).
2) How they meet the financial requirement and which category you are applying under
3) Where you live (or will live) together in the UK - address and property details
4) A short history of the relationship... facts/dates only and how you keep in contact (i.e. you live together)
Since I'm switching from a tier 4, do I need additional proof of our relationship besides the required marriage certificate and correspondence documents? We got married on November 24, but we've been living together since July 2016. Will they need photos of us together or anything like that? Or will the required documents suffice.
You should send a photo of you together anyway (even if you are not switching from a Tier 4) - this is just to prove you have definitely met in person.
The main concern with switching from Tier 4 to FLR(M) is that you might be marrying simply to stay in the UK after your visa has ended, but as you've been living together for 1.5 years and can prove you already have a long-term, established relationship in the UK, you shouldn't need to include much more than that.
However, if you were in a relationship before you came to the UK on your Tier 4, it may be worth including some additional evidence from before July 2016, just to show evidence of your relationship. For example, an earlier photo of you together, evidence of trips to see each other or emails/messages sent to each other.