Early career means more than 5 years of post-doc/teaching experience.
Adjuncts and MA/MFA candidates would be eligible, depending on the award stipulations. Adjuncts are welcome to apply, but I would recommend they speak with specific program staff in their region of interest to determine what their competitiveness may be. Some are completely open to adjuncts and professionals; others are really seeking academics at a certain level in their career within academia. It will vary greatly from country to country.