Exclusivity (Only / Nothing But)

'Only': is it a shortfall, or someone doing the same thing over and over?

Noun ばかり vs Noun しか～ない: ばかり is about repetition or excess and often carries a complaint (ゲームばかりしている). しか〜ない states a bare restriction with a negative verb (千円しかない) and implies the amount is less than you wanted. They are not interchangeable: ばかり cannot count, and しか cannot grumble.

Stressing how little there is, rather than that you have no choice.

～だけしか vs ～しかない: だけしか doubles up だけ and しか purely for emphasis on the restriction. しかない after a verb is a different thing altogether: 'there is nothing for it but to', a lack of options rather than a lack of quantity.

Sizing up a claim: is it merely this, or is it exactly this?

～に過ぎない vs ～にほかならない: These point in opposite directions. に過ぎない dismisses ('nothing more than a rumour'), while にほかならない insists ('it is nothing other than proof'). Both translate as 'nothing but', which is why they get swapped, and swapping them inverts your argument.

Writing the terms of an offer or a rule.

～に限り vs ～に過ぎない: Use に限り. It restricts who or when something applies to (本日に限り半額), which is administrative language, not evaluation. に過ぎない judges something as insignificant and has no place in terms and conditions.