한국어를 조금 말할 수 있어 / 한국어를 조금 할 수 있어.
The two sentences mean exactly the same thing. 하다 is just a shorthand for 말하다 in this case.
Both can be used, but the latter is more common. The reason is because the context is already clear.
Since 한국어 in the beginning sets the context to language or speech, 하다 will trigger the sense of 말하다.
Similarly, if a quoting words like ~다고, ~라고, etc. appears in the sentence, we usually say 하다 in place of 말하다.
As for 진짜/정말, those are the common colloquial terms. 진짜로 and 정말로 are their full fledged, emphasized forms.
Some less colloquial related terms are 참으로(really), 사실/사실은/실은 (speaking of the fact).
There are other literary words too, such as 실로/진실로(really, in truth), 진정으로/진심으로(honestly), etc.