Can I offer a group plan to my full-time employees, and an ICHRA for part-time employees?

Yes, you can! Under ICHRA you can set your employees up by different classes including full-time or part-time. ICHRA regulations allow for an employer to offer both a group plan and ICHRA benefit as long as the benefits are offered to different classes of employees (ie- employees cannot choose between participating in group plan or ICHRA).