Skipping
I don't know what brand/model of internal gear hub you have but one needs to keep the hub in adjustment so that it works properly. It should not freewheel under pedaling force but if you routinely exert high pressure it could cause more problems than would normal riding. "Pushing down real hard" accomplishes nothing but wearing down the bike more quickly (meaning you won't go faster nor get in better shape).

Rusting chain
How fast rust occurs can vary greatly depending on chain, salt and other contamination, weather and storage conditions. Lubrication is done according to need, not time. If the chain starts to look dry or makes more noise (not just squeaking, but rattling also) then it needs lubrication. A properly lubricated chain will rust only in the worst winter/salt conditions.

Loosening spokes.
Spokes that loosen under normal riding conditions indicate a wheel that has not been properly tensioned. If someone just fixes one spoke without attending to sufficient and even tension the problem will reoccur. The only other thing that commonly causes spoke loosening is abusive riding or impact damage to the rim due to road hazards or low tire inflation.