Full day rates can differ depending where you are. It's usually 10-12 hours. Some places regulate film days as 12 hours, some as 10. I tend to work 10 hour days, but if the situation ever arose where 12 hour days were expected, I wouldn't bork and expect 2 hours overtime pay (at hourly rate+50%). That said, here in Aus, overtime loadings are quite high and most will stick to a standard 10 hours in case people aren't all cool about it. We are also required to be paid night loadings for night shoots. Our union dictates standard rates for different crew levels, and this is often a good guide. Most major productions will pay union rates even if crew members aren't part of the union. The union sets a full day at 10 hours.
In terms of half-day rates, I'm still debating whether I make half day rates available.. Sometimes they can be useful for things like table reads, location recces etc, but on the other hand you essentially have a day that you cannot take any other work, but are only being paid half your rate for. I'm sure there's something in the union documents about half-day rates, I'll have to sift through them again..