I'm in the process of learning F#, too, and I somehow managed to make a functional solution to problem two take more lines of code than what I wrote in C#. There must be a more elegant way to tackle this one.

let rec fib x =
    match x with
    | 1 -> 1
    | 2 -> 1
    | x -> fib (x - 1) + fib (x - 2)

let newList = []

let rec fibSeqConstructor fibSeq i limit=
    let nextFib = (fib i)
    if nextFib < limit then
        let fibSeq = fibSeq @ [nextFib]
        let i = i + 1
        fibSeqConstructor fibSeq i limit
    else
        fibSeq

let problem2 =
    (fibSeqConstructor newList 1 4000000)
    |> Seq.filter (fun x -> x % 2 = 0)
    |> Seq.fold (+) 0
printfn "The sum of all Fibonacci sequence numbers below 4,000,000 is %i" problem2