Effects depending on an impossible effect?
If a creature explores an empty library, the creature gets a +1/+1 counter and nothing more happens. There is no general answer to what happens with multiple, partially impossible instructions.

The relevant rules of the explore mechanic are:


  701.39a Certain abilities instruct a permanent to explore. To do so, that permanent’s controller reveals the top card of their library. If a land card is revealed this way, that player puts that card into their hand. Otherwise, that player puts a +1/+1 counter on the exploring permanent and may put the revealed card into their graveyard.


You can't reveal a card because there are none remaining in the library. Therefore, no land card has been revealed, so you can't put it in your hand and you continue resolving the ability with the "otherwise" instructions. Note that the "otherwise" condition refers to both the "card" and "card type: land" requirements that both have to be true to make you take the first branch of the instructions. 

In the second branch, you do as much as possible: You put a +1/+1 counter on the creature and, since you didn't reveal a card, can't choose to put the revealed card into your graveyard, so nothing happens on that instruction.

It would have been possible to word the second branch so that the creature gets a counter if and only if you actually put a card into the graveyard, i.e. the creature would not get a counter on exploring an empty library. In that case, it would get another instruction branch nestled into the second branch:


  Otherwise, you may put the revealed card into your graveyard. If you do, put a +1/+1 counter on this creature.


Because of the flexibility of the rules, it's impossible to give a general answer as to what happens when there are multiple instructions and some of them are impossible. It always depends on the wording of the card(s) involved.