Can I cast Hidden Blade if my opponent casts Thrill of the Hunt, and can I still target the same unit?

To answer your question, we need to look at the timing of when targets are locked in for spells.

According to Rule 355.14.b and the general rules for targeting, targets for a spell are chosen and locked in when the spell is finalized and added to the chain.

Here is the sequence of events:

1. You play Hidden Blade: You choose a target unit at a battlefield and add Hidden Blade to the chain. At this point, the target is locked.
2. Opponent reacts with Thrill of the Hunt: Your opponent plays Thrill of the Hunt in response to your Hidden Blade.
3. Thrill of the Hunt resolves: Thrill of the Hunt banishes the friendly unit and then its owner plays it to a battlefield.
4. Hidden Blade attempts to resolve: When Hidden Blade attempts to resolve, it checks the legality of its target. Because the unit was banished and then re-played, it is considered a new game object. Therefore, the original target is no longer present at the battlefield (it has moved zones and returned as a new object), making the target illegal.

Result: Because the target is no longer legal, Hidden Blade will "mistarget" (as described in Rule 359.3.e.9). The instruction to kill the unit cannot be followed, and the effect will not resolve. Consequently, no unit is killed and no cards are drawn.

In short: No, you cannot "re-target" the unit. Once the target is locked on the chain, you cannot change it, and because the unit left the battlefield and returned as a new object, the original target is no longer valid.