Re: work fixed time?
I have a slightly different thought on this.
If you work a regular schedule, it may imply that you work regular "office hours." More or less, 8 in the morning to 5 in the evening.
On the other hand, you could, work the night shift, for example, from 3 pm to 3 am, four days a week one week and three the next. That would be a fixed schedule -- it doesn't change from that two-week cycle, but I wouldn't call them "regular hours."
Even so, you could still say "Well, my regular hours are 3 pm to 3 am, but I can change my shift that week if you need me to."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.