According to Longman Dictionary of Contemporary English, "sometimes" has a meaning similar to occasionally. "Sometime", on the other hand, can be used when you do not know exactly when the time is either in the future or in the past.
Therefore, "Sometimes, I study English" is equivalent to "Occasionally, I study English". "I will study English sometime in this month" is equivalent to "I will study English in this month, but I cannot tell you exactly the day is"
In addition, I cannot find any explanation about "some time". This is because it is not a phrase word. It is similar to "some milk", "some money", "some fun" etc. In the words, the "some" is used to describe the amount of the thing in these cases.
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Written by: Xaivier Chia
Reference:
Longman Dictionary of Contemporary English 4 with CD
