Special Summoning “Drill Warrior” and adding 1 Monster Card to your hand do not happen at the same time. You Special Summon, then add the Monster Card to your hand. “Bottomless Trap Hole” cannot be activated.
You do not target the Monster Card, you return to your hand.
The effect of "Drill Warrior" which halves its ATK gives it the ability to attack directly. The effect does not force "Drill Warrior" to attack directly during that turn's Battle Phase, so "Drill Warrior" can still attack a monster.
When resolving the effect of a banished "Drill Warrior" which Special Summons it, you can Special Summon "Drill Warrior" even if there are no monsters in your Graveyard. However, after Special Summoning "Drill Warrior" you cannot resolve the effect which adds a card from your Graveyard to your hand, so cards like "Bottomless Trap Hole" may be activated.
When resolving the "You can discard 1 card, and if you do, banish this card." effect, if you cannot discard from your hand - for example, you chained "Full Salvo" - then you cannot banish "Drill Warrior". However, when resolving that effect, if "Drill Warrior" cannot be banished - for example, "Imperial Iron Wall" was chained - then you still discard 1 card.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.