Underwurlde is right, at least in some aspects...the airpump (with an airstone) does not put oxygen into the water itself, but rather promotes gas exhange of the water by aggitating the surface water. I would not know if this is good or bad for plants since I am by far not an expert on them.
IMO and IME, you can keep your lights on in the tank as much as you want, however you would have to think more about limiting lighting depending on how much algea is growing or if you are experiencing cynobacteria (blue/green algea) since these need light to grow and many people find that limiting the amount of time lights are on can have a direct effect on the algea growth....
However, I have read A LOT about how plants themselves can limit algea growth because they 'suck' the nutrients out of the water that the algea needs as well, creating a sort of competition for nutrients and plants typically win out.
So, in short, there is no definitive answer to your question, but I would suggest keeping them on for longer than an hour (with betta fish being the exception) for your plants of course, but less than for 24 hours since your fish will need a simulated 'night time' in order to rest and 'sleep'. This also is the time that most algea eaters are most active (plecos especially) and so you should think about turning the lights out if you are keeping any nocturnal fish.
