There is indirect PvP aspects in Planetary Interaction, and soon there will be direct PvP aspects with the release of a console game called DUST514.
The indirect PvP aspect is fighting over resources. This was only turned on in some of the later patches in the Incursion. On each planet there is only a limited number of the resources in the ground, which only refill at a certain static rate. The planet will support some (unspecified) minimum amount of resource being extracted, then after that it will deteriorate. This means that too much concentration in the area will deplete the resource for all players pulling that resource out of the ground at that place.
The direct PvP will come later when the DUST514 console shooter game comes out. Exact details haven't been confirmed yet, but the base premise of it is that people playing Eve Online will be able to somehow ask players in DUST514 to somehow disrupt other Eve Online players Planetary Interaction networks.
There are usually two types of Planetary Interaction (PI) setups : Extraction and Factory setups.
With Extraction setups, PI doesn't really require any sort of ongoing ISK costs to run besides export fees of planetary products, therefore all PI here should be "profitable". In High-Sec you won't get very high extraction rates at all, and they will be highly contested, which means not very profitable on a "ISK-per-time-invested" basis. Lo-Sec can be better, but Null-Sec and Wormhole planets can be quite lucrative. There is a larger risk in transporting the PI products from these lower security areas of space though.
With Factory Setups, people can make a fair amount of ISK by making PI setups in High Sec that purely concentrate on turning lower level cheaper PI products bought from the market into higher level more expensive products. You'd need to figure out what is profitable here and what isn't as it would also be quite easy to lose a lot of money doing this if you chose the wrong products, or the sell prices of the high-end product dropped unexpectedly.
In terms of investment of training time, it doesn't take too long to get decent PI skills. Anywhere between a few days for some basic skills to a couple of months to be able to run multiple planets with high level command centres depending on how much PI you want to be involved in.
Short of building and maintaining a POS, you can use this search tool to find all stations in the EVE universe with particular characteristics.
You will probably need to use in-game tools to identify stations with spare slots, but this should at least make finding the stations a bit easier.
Best Answer
Straight from the EUNI wiki class Overheating 101 :
Repairing heat damage
There are two ways to repair heat damage to modules.
The first is simply to dock up at a station with a Repair Shop, and use the station service to repair all your modules. [snip] Using a repair shop in this way is the only way to repair broken modules.
If your modules are merely damaged, and not broken, you can repair them in space using a substance called Nanite Repair Paste. To use this, you simply need some of it in your cargo hold, and when right-clicking on a damaged module you will see an option to 'Repair Module'. Note that you don't need any skills at all, not even Thermodynamics, to be able to repair heat damaged modules using this paste. A module under repair cannot be used, and no other modules - on any rack, high mids or lows - can be overheated whilst one or more modules are being repaired. You can however repair and reload a turret at the same time. You can repair a bit at a time, by right-clicking on a repairing module and selecting Cancel Repair.
In a very similar fashion to station repair costs, repairing higher meta level items or large/medium items will consume more paste.
There are two skills that improve your repair efficiency:
Nanite Operation - which reduces the amount of Nanite Repair Paste required by 5% per level, thus causing you to use less paste
Nanite Interfacing - which increases the amount of damage repaired per second by 20% per level, thus making your repairs faster
Neither of these skills are required to use nanite repair paste, they only make it more efficient. You have no indicator of how long a repair will take, or how much paste it will use, until the repair is finished, and there are no "partial" repairs. As one example, with zero Nanite Interfacing skill it can take approximately 4 minutes to repair a T1 light missile launcher that is 90% damaged. With Nanite Operation trained to III, the repair uses one unit of paste to heal 35 hitpoints of module damage.
An unfinished repair will cancel following a gate jump or other session change. Despite the high (5M ISK) cost of the Nanite Interfacing skillbook, it's worth considering that it's uncommon during an E-Uni roam to stay in one system long enough, for a repair to complete with zero skills. Safely and quickly docking at a station with repair facilities may be your only opportunity to keep pace with the fleet, but your FC should be made aware of your intentions first!