When I play Heedless Resurrection and I kill a Rhasa, which is at a battlefield, can I play the unit, which I can play with Heedless Resurrection at the battlefield, where Rhasa was before killing it?

Yes, you can play the resurrected unit to the battlefield where the Rhasa was.

According to the RiftJudge FAQ #9753 regarding Heedless Resurrection, even if you kill your only unit at a battlefield to pay the cost, you do not lose control of that battlefield while Heedless Resurrection is on the chain. Because there is still an item on the chain (the spell itself), the cleanup process that would normally cause you to lose control of the battlefield does not occur.

Sequence of Events

1. Play the Spell: You announce Heedless Resurrection and place it on the chain. This creates a Closed State.
2. Make Choices: You choose a valid unit from your trash to resurrect. Note that per RiftJudge FAQ #9523, you cannot choose the Rhasa you are about to kill because it must already be in the trash to be a valid target when the spell is played.
3. Pay Costs: You pay the additional cost by killing Rhasa. Rhasa is moved to the trash.
4. Battlefield Control: Even though Rhasa is now in the trash and may have been your only unit at that battlefield, you retain control of the battlefield because the spell is still resolving on the chain (Rule 187.4.c).
5. Resolution: The spell finishes resolving. You play the chosen unit from your trash. Because you still control that battlefield, it is a valid destination for the unit.

This is my interpretation based on Rule 187.4.c and the provided FAQ #9753. No other official FAQ contradicts this specific sequence.