I frequently have dealt with recruiters both in my local time and in another time zones. What it is expected on a recruitment negotiation process is some flexibility on both sides, and both remembering the person on the other side is busy with a job, a family and tasks to honour.
I advise trying to coordinate sensible times with recruiters as they also have a personal life and office hours. Especially in Germany and the UK, if working in an office, people are adamant about their 9 to 5 schedule as a rule.
Here in Lisbon, there are a lot of people that is from other cities, and as such, I avoid asking for Friday afternoon interviews unless the interviewer is fine with it. That said, I have had earlier-later calls from recruiters. Locally here in Portugal there is also a culture of working late, so 6-7PM face-to-face interviews are quite common, as the "official" dinner time is around 8-9PM.
I remember also having face-to-face interviews on a coffee shop, on Saturdays, or even in an hotel cafeteria at lunch time (and getting the job in two of them). Recruiters or upper management can be very flexible when they are really interested on you.
You could take a cigarette/coffee/snack break to talk with them, if it is a short screening call, or use the lunch hour for longish interviews over the phone. Another possibility is leaving earlier in a pre-arranged day when more advanced in the recruitment process, and if unable to reach home in a sensible time frame, making the interview call in a local coffee/Starbucks shop for skype interviews.
As for myself, as I live nearby, I often shorten the day, and/or enter the job early, so I can reach home in a sensible time frame (for me and them).
If the headhunter is willing to go the extra mile, late night or Saturday mornings interviews are not entirely unheard of. However, I would advise to wait for them to offer the possibility.
For confirming and rescheduling booked screening call/interviews, we live in a connected world, and any sensible interviewer will make use of instant messaging/linked.in messages during work hours to relay you scheduling changes ahead of the arranged time. Seasoned professionals, when calling you, often the first think they ask is if it is the right moment to talk.
About the theme of interrupting the work day abruptly, I advise reserving that for the final phase(s) of the recruitment process - there are only a few hours/days in a year we are able to take off. An headhunter saying you will have to have that flexibility from the get go is not a good sign.
However, if an interviewer is not willing to work with you to book a time both of you are comfortable with, maybe you should say you are not comfortable or at ease with the process and move on.