Can I use a 2.4 GHz rated parabolic MIMO antenna for 700 MHz Verizon 4G LTE data?
Can I use a 2.4 GHz rated parabolic MIMO antenna for 700 MHz Verizon 4G LTE data?


The gain of an antenna, that is, how much it focuses in one direction, is pretty much proportional to its size divided by the wavelength.

Generally, antennas don't work (well) for frequencies they're not designed for, but you can consider a parabolic dish more of a reflector than an actual antenna – the feed (which is mounted in the focal point) is what actually converts the electromagnetic wave from free space to a coax waveguide (or vice versa).

So, replace the feed with something that works for 700 MHz and you got a directive antenna that's roughly only 700/2400 = 7/24 ~= 1/3 as directive as it would've been for a signal at 2.4 GHz.

Now comes the problem: you don't seem to have such a feed (and you're right, you need a multi-band antenna as feed). 

In this situation, you'd just buy a cellular-optimized multi-band antenna that has some gain in itself: it typically will have less gain than what you'd get from a well-matched dish, but considering this is all a bit impossible to calibrate and do right, it'll probably work much better than trying to attach a low-gain multi-band feed to your dish.

Generally, what you want to do is quite possible illegal: in many legislations the power times the gain is limited, and if your phone is legal with the little gain its antenna has, it's probably illegal with the gain of a highly directive antenna. 


  Will the same Verizon tower switch me from 700 MHz to one of their higher frequencies with better reception?


Only the base station configuration of Verizon's cellular infrastructure can answer that. But, generally, the lower the frequency, the better your reception is over a long-distance link: so, 700 MHz is pretty much the best you can get.

"as some people report": Um. "some people" are a terrible source.