No it won't make any difference to the plant. Most times it gives you a better shaped plant if you remove them.

I separated them today. I just pull them apart - both have roots. Hope they'll both heal well.

Should I have used a knife?

The soil is quite moist now. How long should I wait to water them?

When I repot I usually soak the pot for a few minutes to get all the air out then water when needed.
Your mum will probably send out more pups. Give her some fertiliser to help.
If they come apart easily a knife isn't necessary. I usually try to pull the pups off before using a knife.

Dont over fertilize if you dont want all green plants when they should have color in the leaves. Small regular doses are better than dumping fertilizers.