Based On (In Accordance With)

Naming what a decision or a document was built on, not who said it.

～に基づいて vs ～によれば: Use に基づいて. It says the thing was constructed in accordance with a rule, a principle or data. によれば cites a source for a piece of information ('according to the paper') and cannot describe how something was made.

The basis is an assumption being taken as given, not an established rule.

Noun を前提として vs ～に基づいて: Use を前提として. It marks something granted for the sake of what follows, which may yet turn out false. に基づいて treats its basis as solid ground, so it quietly asserts more than you may mean.

に即した or に即して: which one attaches where?

Noun に即して Verb vs Noun に即した Noun: に即した modifies a following noun (実情に即した対応), に即して leads into a verb (実情に即して考える). One word, two slots; the meaning does not change, but the wrong form will not attach.