In the case of Fire Aspect, we need to know the material of the sword you are enchanting, so I'll assume diamond, in which case the minimum level required to get any level of Fire Aspect is 4, with a 0.2% probability; if you enchant at level 10 instead the probability rises to about 10% (1.8 has a slightly higher chance than 1.16). For Fire Aspect II the minimum level is 22 (0.1% for both versions) and the best level is 30, with a 13.5% chance in 1.8 and a 15% chance in 1.16.
For Punch, the minimum level is 10 for Punch I and 27 for Punch II; in all cases 1.16 has a lower chance at lower levels and a higher chance at higher levels. Level 30 is generally the best level to enchant at; however, in some cases the chance of an enchantment can decrease due to other enchantments displacing it (in 1.8 the highest overall chance of Punch is 30.9% at level 16, then it decreases to 21.4% at level 22 before increasing to 24.9% at level 30. In 1.16 it peaks at 24.1% at level 16, then it decreases to 20.1% at level 21 before increasing to 25.6% at level 30. Note that Punch II reaches a maximum at level 30 and you have a higher chance of other enchantments so level 30 is still better).