Question about my LS2

[Lonnies Performance]

To clarify, they are O2 sensors.

If the engine was properly tuned, it will run fine with them disconnected, but the ability to correct for various conditions would not be possible.
Yes, you should plug them in. Without diagnostic abilities, you have no way of proving the tune is good.

Tuning for E85 is not a matter of just putting different fuel in & tuning.
You often (most likely) need larger injectors & possibly a modified fuel system.
.
Also, since E85 is not tightly controlled (Ethanol content varies greatly), so your tune may vary from tank to tank.
The O2 sensors correct somewhat but the ideal way is with a flex fuel sensor that may or may not be compatible with the ECM in your vehicle.

Lots of different tuning software available, but HP Tuners is the most common which makes it easier to share in the knowledge base online.
I would suggest you start doing a lot of research, before investing money in the software to assess your ability to tune your vehicle.
There are lots of good tuners that may be able to set you up for less money than the investment to do it yourself... unless you have multiple vehicles to do.