I have the same lens, same camera. I will tell you that lens needs lots of light, but that also depends on the situation you have. You say very well lit, but that may not be enough for the lens. I actually switched to a 70-200 f4, shorter but its a true f4 through all focal lengths. The issue with the 70-300 is on the long side its a f5.6 which is another stop difference and will require that much more light to freeze the action. It can be done, but you will have to play with the settings.
Sports pictures you need to have your shutter speed above 500 usually to freeze action and as you loose light you look shutter speed unless you up your ISO. Upping the ISO creates another situation that for the most part can be dealt with in your post processing ( work on the computer), this issue is Grain ( Noise ) in the pictures.
I would highly suggest you get out before season and play with the settings, get really used the camera and the lens to see what it wont do. You will also want to get as close as you can to the action to improve your image quality. On the longer end of this lens pictures have a tendency to get soft and the low light will only compound this.
I love the 70-300 in the sun, but at night it wasnt my best friend and I have improved my pictures by simply changing to the 70-200 f4.
Now if you really want a great lens for night time shots then you need to save for the 70-200 f2.8.
I still have to up my ISO and keep the aperture as wide as I can, which is f4 in order to get decent shots but I still get grain. I have some very high ISO shots that I kept but for the most part I just know when its time to put the camera down or try and get closer to the action.
Sorry, but I dont have any examples that I can post to show this. But the best advice I can give is to get out and shoot, even if its football practice.
As far as the manual/auto question, leave all in auto. If you get a manual lens then lens will be manual and your camera body motor will take over. I have never heard of damage, only frustration with having one or the other because the user was unable to focus.
I will tell you that the 18-105 is a lens that surprised me with sports shots. If I am not shooting sports then its the lens that I leave on. If I am shooting sports then I use it for team pictures or complete field shots, its a very useful lens and the quality shocked me for a kit lens.
I honestly didn't have the knowledge of the camera last football season to really have pushed this camera so I am looking forward to this season but my go to lens will be the 70-200 f4. As a matter of fact my 70-300 sits on my desk and has for months because the lack of focal length hasn't been a huge issue because you can always crop on the computer. Although I might get slapped on here for saying that. You just really have to learn your camera and the limitations of both the equipment and photographer.
Also look at the sports section here, although not many shoot sports on here there are a few of lying in the brush waiting for questions.
Just get out and shoot in a situation that is similar to the games and try different settings till you get it down.
Sorry to be so long winded and hope you find it useful.