Combine two text fields line by line

You can create a new formula text field using this formula:

List("\n",
  List(" ", Part([Alpha], 1, "\n"), Part([Dates], 1, "\n")),
  List(" ", Part([Alpha], 2, "\n"), Part([Dates], 2, "\n")),
  List(" ", Part([Alpha], 3, "\n"), Part([Dates], 3, "\n")),
  List(" ", Part([Alpha], 4, "\n"), Part([Dates], 4, "\n")),
  List(" ", Part([Alpha], 5, "\n"), Part([Dates], 5, "\n"))
)

Once you confirm this produces the desired result, you can convert the text formula field to a text field and delete the original [Alpha] and [Dates] fields.

Notes:

(1) You have to implement this formula assuming a specific maximum on the number of lines in your data (n=5 for my formula).

(2) The List() function is used to avoid adding spaces if [Alpha] or [Dates] don't have the same number of lines. If you do have the same number of lines in all your data, you can use this shorter formula:

Part([Alpha], 1, "\n") & " " & Part([Dates], 1, "\n") & "\n" &
Part([Alpha], 2, "\n") & " " & Part([Dates], 2, "\n") & "\n" &
Part([Alpha], 3, "\n") & " " & Part([Dates], 3, "\n") & "\n" &
Part([Alpha], 4, "\n") & " " & Part([Dates], 4, "\n") & "\n" &
Part([Alpha], 5, "\n") & " " & Part([Dates], 5, "\n")

(3) I have to tell you that I hesitate to answer using native formulas as I feel like I am enabling bad practices. The formula language is very limited and in today's world you should not have to make assumptions such as the maximum number of instances of some characteristic. The equivalent JavaScript implementation is much more succinct and covers more cases than your particular [Alpha] and [Dates] fields. In the most helpful way but using strong language I have to tell QuickBase to enter the modern world - the product will be a lot more successful if you re-channel your userbase's resourcefulness from coming up with workarounds like this to working with more expressive product features. Replace the formula language with script.