You wouldn't be able to cast counterspell in the first place
As others have pointed out, you can only cast the spell if the condition to trigger the reaction have been met, in this case
When you see a creature within 60 feet of you casting a spell
However the Distant Spell Metamagic description is the following for a spell that has a range that is not touch:
When you cast a spell that has a range of 5 feet or greater, you can spend 1 sorcery point to double the range of the spell.
Meaning that you must already be able to cast the spell to apply the metamagic onto it. Of course, you could then double the range of counterspell to 120ft, but it would still need the trigger of seeing a spell being cast within 60ft to use it.
The same ruling would technically apply to Feather Fall, although your distant spell might allow it to reach creatures up to 120ft away as long as one of the targets for your spell is within the initial range of 60ft.
Homebrew ruling and justification (Personal opinion)
Although this is per RAW, it does seem that per RAI the 60ft requirement is correlated to the range of the spell. In fact, I prefer the D&D 5e wikia version, which seems to state that the trigger is simply seeing a creature cast a spell. In which case, your DM could rule that your ability to use a Distant Spell Metamagic option does extend the range of the trigger as well as the range of the spell itself.