I just got mine and it was also 60% charged. I started using it right away and didn't fully charge it. The salesperson never told me that it needed to be fully charged before first use. I even said to her that it has enough charge and I can use it right away and she said yep.
What does not fully charging it do to the phone?
Nothing. You'll be fine.
Also, is it bad to use it when it's charging?
Maybe, but only in one case: if you have it pugged in to a charger that supplies too little current, you could have a situation where the battery is draining faster than the power can supply it. I've seen cases on other phones (plugged in to a USB port that supplies a small level of current) where the phone was actually draining faster than it would have if it wasn't plugged in. The battery pack was at a low charge and the circuitry was set to supply a lot of voltage to the battery pack to charge it faster when it was below 15%. This was a phone from several years ago, and I'm not sure if the Maxx would suffer from this.
Still, batteries do not like being overheated - it tends to wear them out faster - and if you are charging your phone while using it in a high power situation - say, while navigating in the car and plugging in to charge - that might be bad for the battery pack. In that case it would probably be better to navigate on battery and then plug in later to charge it. But, if you are on a trip of several hours and the battery would drain too much, you may have no choice.
Again, I believe that over a 2 year period with a battery of this size in the Maxx, you should be fine.
And lastly, is it bad to charge when there's 50% charge left for example?
No, that's fine. I believe that Li-ion battery packs actually do better with small charges like that rather than persistent deep drains and deep charge cycles.
I suggest this: plug the phone in while you sleep. If you are worried about battery life, and you don't need the phone to be powered on while you are sleeping, power off and then plug in to charge. When you wake up unplug and power back on. Repeat when you go to bed again.