When I play Beast Below and target my Yordle Explorer for the effect, do I still draw the card with Yordle Explorer?

Yes, you will still draw a card with Yordle Explorer.

Here is the breakdown of why this interaction works:

1. Triggering Yordle Explorer: Yordle Explorer's ability triggers "When you play a card with Power cost [2] or more." When you play Beast Below, you are playing a card with a printed Power cost of 2. This satisfies the condition for Yordle Explorer's ability to trigger.
2. Chain Resolution: When you play Beast Below, its "When you play me" ability and Yordle Explorer's "When you play a card..." ability both enter the chain.
3. Effect Independence: Even if Beast Below's ability targets your Yordle Explorer and returns it to your hand, Yordle Explorer's draw trigger has already been placed on the chain. According to Rule 356.3.e.10 and the general principles of chain resolution in Riftbound, once a triggered ability is on the chain, it resolves independently of the source that triggered it or the current state of the unit that triggered it.

Therefore, even if your Yordle Explorer is returned to your hand by the effect of the Beast Below you just played, the draw trigger will still resolve successfully.