Can a pariticipant in a qualified plan name a charitable trust as beneficiary?

Yes. It is not uncommon to name a trust as a beneficiary.

Yes, a charity can be named as a beneficiary of a qualified plan benefit. However, if the participant only wants part of the account to go to charity and the rest to go to individuals or a qualifying trust, naming the charity could lead to unintended results. When the participant reaches his required beginning date and must start minimum required distributions, the naming of the charity will result in the requirement that the participant use only his life expectancy, rather than a joint life expectancy with an individual beneficiary. This could result in a larger MRD than intended.
A benefit of naming a charity or private foundation is that when the qualified retirement funds are paid to it, they do not generate income tax to the charity as it is tax-exempt and the benefits pass estate-tax free as well.

Can a rollover IRA beneficiary designation be drafted using separate account language leaving a percentage to a trust for individuals (i.e., 75% to the trust), assuming it meets the trust requirements to be a "designated beneficiary", and the remainder (i.e. 25%) to a charity and have the minimum distributions to the owner be calculated on the basis of the owner's and individuals' joint life expectancies as to the 75% and the owner's sole life expectancy as to the 25% going to charity?

As a follow-up to the original message, check the plan language regarding beneficiary designation as some plans limit beneficiaries to individuals.