Q:Independence from what?
A:Independence from Japan. Legally speaking, there can be no other way, unless you are betting on Japan and the Allied Powers voiding the SFPT, which contains the legal source of Korea's independence from Japan as well.
Q:Who would recognize the Republic of Taiwan?
A: Independence does not necessarily entail a republic. A republic does not necessarily entail independence.
A republic can be autonomous, or dependent as well. Likewise, an independent country doesn't need to be a republic. It can be a federation or a territory.
Q: Does ROC claim to rule China?
A: No it doesn't. You can not find it anywhere in ROC's articles of incorporation (aka constitution) or self-regulations. Claiming to rule any place is not a basis of this organization. Claiming to rule china is a political belief of certain people, but it is not laws or regulations. Read the text.
Q: Does whether or not anyone recognizes roc has anything to do with recognizing Taiwan?
A: No. Any government can recognize Taiwan regardless of whether they think Taiwan is a sovereign state or not. Recognition of a Government of Taiwan does not depend on recognizing Taiwan as a sovereign state. If you recognize Taiwan as an Autonomous Territory, you can still recognize the government of Taiwan as a legitimate government.