The conjugation of 〜ぬ (or, more properly, 〜ず) is as follows in classical Japanese:
- Predicative form (終止形): 〜ず
- Attributive form (連体形): 〜ぬ
- Adverbial form (連用形): 〜ず
- Realis form (已然形): 〜ね
As you can see, it is somewhat defective; the missing conjugations are sometimes supplemented by the corresponding forms of 〜ざる (more properly, 〜ざり). In modern western dialects, the predicative form has been replaced by the attributive form, which has indeed been contracted to 〜ん. This page has more details (in Japanese).
The classical ways of forming the past tense of 〜ず are 〜ざりき and 〜ざりけり (and in older writings, 〜ずき and 〜ずけり), but in modern western dialects it is supposed to be 〜なんだ. Apparently 〜ざった and 〜だった are also attested. Nowadays one also sees 〜んかった but this should probably be regarded as a contraction of 〜なかった rather than a continuation of something classical – the 日本語国語大辞典 only has citations starting from the late 19th century.