She could be angry. Hermione is used to being in control of situations through her knowledge and planning. Having a Death Eater surprise her disrupts that. So she might feel angry at the intrusion and at the threat this Death Eater poses to her safety and the safety of those she cares about. This anger could fuel her actions in the encounter, making her more aggressive in her defense.
She might react with caution at first. Given that Death Eaters are known for their cruelty, Hermione would be smart to be on her guard. She would likely start by gathering information about the escaped Death Eater, like his known abilities and any possible weaknesses.
Well, one possibility is that Hermione uses her quick wits and magic skills to defend herself. She might immediately cast a stunning spell or a protective charm. For example, she could use the Protego spell to create a shield between her and the Death Eater. Then, she would likely try to find a way to escape or call for help. Maybe she'd use her Time - Turner (if she still has it in the fanfiction context) to go back a few minutes and avoid the encounter altogether.
Over time, if she couldn't immediately escape, Hermione would try to influence the Death Eater. She would use her knowledge and strong moral compass to show him the error of his ways. She might start by having debates with him about the Dark Arts and the ideology of the Death Eaters, hoping to make him see the light.
She could also try to reason with the Death Eater. Hermione is known for her intelligence and ability to think on her feet. She might try to appeal to any sense of humanity the Death Eater might have, reminding him of the consequences of following Voldemort's evil path.
Hermione would likely try to outwit them. She has a sharp mind. She might use her knowledge of magic, both dark and light, to find ways to counter the Death Eaters. For example, she could use spells that they wouldn't expect or find loopholes in their dark magic.
She might become extremely angry and cut off all ties with Draco immediately. Hermione is a strong - willed character, so she would not tolerate betrayal easily. She could use her magic to create some sort of barrier between them, magically locking him out of her life.
In such fanfiction, Hermione being a Death Eater could lead to some really interesting character developments. Maybe she has a hidden past or some sort of brainwashing that led her to this side. It would also change her relationships. Ron and Harry would probably be in a state of shock and disbelief, and their quest to defeat Voldemort would become even more complicated as they now have to deal with a powerful Hermione on the wrong side.
Hermione's character development is evident in multiple ways. Firstly, her confidence has grown. She's no longer the shy girl who might hold back her thoughts. When she speaks up at the Death Eater trial, she shows that she has complete faith in her knowledge and judgment. Secondly, her sense of justice has deepened. She is willing to take risks to ensure that the Death Eaters are held accountable for their actions. This shows that she has evolved from just a studious witch to a defender of justice in the wizarding world. Also, her ability to stand up against the dark forces on her own indicates her independence has also developed. She doesn't rely solely on Harry or Ron but takes the lead in this crucial situation.
Hermione would likely be a mix of disappointed and worried. Disappointed because Harry is usually responsible, and worried because she cares about him. So she'd probably try to figure out why he got drunk in the first place.
She probably comforts him right away. Hermione is a very empathetic person. She might give him a big hug and let him cry on her shoulder.