Problem is that the spindle motors on the Series I are most likely not "inverter rated". Problem is that when you want to slow the spindle way down with the VFD, you need (generally) more horsepower from the spindle motor, yet you have much less cooling from the internal fan on the spindle motor. So it's probably better to use the variable speed pulley system to get down to slow speeds, and use the VFD to get higher speeds.
Several people removed the back gear completely and run a fixed belt ratio.
2. My way oiler was a Bijur, and I believe that it will run on either, but am not certain. My way oiler was shot, replaced it with a very similar oiler made in Taiwan, for under $200. The Bijur cost more than my house.
You do need to check and make sure all the lube metering units are actually working. If the mill has sat for any length of time, the way oil turns to thick gum and plugs the metering unit. On my mill, of 32 metering units, 31 were plugged up. YMMV
3. Have no experience (yet) with the coolmist system, but my previous owner seemed to like it. Have no idea if it's a Bijur or not.