I'm pretty new to the ATV/UTV world myself, but I've heard in the past that if the transmission is hard to get into low range, its usually due to the shift linkage binding, being bent, or not properly adjusted.
For the cutting out when diff-lock is engaged that's due to the diff-lock not being fully engaged. This could be due to a problem with the differential internals and if it happens all the time you'll probably have to take it in and have it serviced unless you know how to work on the mechanism yourself. However if its just once in a while, its pretty common sometimes that the diff-lock takes a few seconds to engage what I've found that helps is to turn the steering wheel while engaging the diff-lock mode. Once its engaged (the diff-lock light will become steady and not flashing anymore) it should be able to gain speed.
I'm not familiar with the older models but I think they had some sort of governor on them to limit full throttle acceleration when in diff-lock mode which would cause the machine to cut out at a certain speed.