Using a IR2125 to drive a MOSFET gate
I am not sure the term v-offset has universal meaning. The best way to tell is to look at the Recommended Operating Conditions (on page 2 of the datasheet), it listed Vs (a specific pin label) can operate up to 500V max. In conjunction with a note above that all voltages are referenced to COM, it is a positive indication that the driver is designed to operate up to 500V.
On page 3 of the datasheet, there are specifications of the "IN" pin -- VIH and VIL indicate 5V TTL levels; I-in+ and I-in- indicate low current requirements meaning it can be driven by any logic output.
t-on and t-off are propagation delays and have some bearings on the maximum frequency, they are also important when you have to time a bridge to minimize shoot-thru. But for the overall maximum switching speed of the MOSFET, the rise and fall time (t-r, t-f) play bigger roles. In most cases, you don't want to operate near the "maximum" switching rate because it would be too inefficient, and also too "non-linear" if that is important.
The current limit feature operate by sensing the voltage difference between the CS and Vs pins. The threshold values are given on page 3 as V-CSTH+ and V-CSTH-, with the typical value being 0.23V. As an example, connect a 0.1 ohm resistor from CS to Vs as in the diagram on the first page. When the current through the resistor gets to 0.23V/0.1ohm = 2.3A, the current limit would kick in and turn off the HO pin.
It is a cheaper circuit for low side. The gate drive (and supply) voltage has to match that of the MOSFET and is not necessarily 5V.