Does a DPOA allow a caregiver to deal with a revocable living trust where the elderly parent is the sole surviving Trustee?

The answer is, that it depends on what both the POA says AND what the trust says. In general, the Trustee of the trust has power over trust assets. The DPOA MIGHT give power over non-trust assets. There is a huge variation in POAs though. Some work now. Some require incapacity. Some only allow for one specific thing to be done. Others allow for everything underneath the sun, including self-dealing transactions. You ought to take the trust and DPOA to a local attorney for a free consultation to interpret the instruments. Also, it is totally conceivable that different documents are now needed. Why? Not only to avoid Probate and Conservatorships, but also to take advantage of Medicaid and/or VA Benefits.

The trust document itself my address successor trustees. Get hold of of a copy and read it carefully.

Yes they can, but should do so with an attorney's advice and of course the transaction should be free of any hint of conflict of interest.

Typo, that should be sell something in the Trust

If my mother is the sole surviving trustee of a Revocable Living Trust and she has granted the caregiver a Durable POA for financial affairs, can the caregiver act as the Trustee and see something in the Trust?

The DPOA can sign documents in accordance with the wishes of the person who granted the DPOA. BUT, the DPOA cannot sign something that would benefit themselves or pay themselves, that would be a conflict of interest.