Right...well I work on the Formula Student team at my university (University of Birmingham - UK) and more specifically the engine group.
With regards to wings...yes they are allowed, but it's very difficult to validate their usefullness. A BIG thing about the FSAE competition is you have to be able to tell the judges why you chose to do something a certain way. This usually means test data of some kind, or measurements that have been made. Proving wings are usefull is therefore very hard as it requires lots of expensive wind tunnel time and testing which is something very few FSAE teams have. Due to the low speeds you usually have to have very high angle wings which are heavy and produce a lot of drag. In the dry there is very little difference between a winged car and a non winged car. In the wet however, those with downforce are significantly quicker. What a few teams are starting to do now is to develop splitters and diffusers to help underbody flow. I personally think these are the nicest solution to downforce on an FSAE car.
Engine wise....we are hugely limited by the rules. A 20mm restrictor has to be placed BEHIND the throttle. This is the absolute worse case scenario when it comes to restrictors. Turbos are very difficult to add to this system as when the throttle is shut the turbo keeps spinning. It generates a huge vacuum in the air plenum and as we found out, tends to do things like suck the oil out of the bearings in the turbo. Normally the way round this is to have a huge air box which results in a large reservoir of air. In most motorsport where the restrictor is placed before the throttle(s) this is OK. However, when the restrictor is after the throttles you have all kinds of problems. If you have a a big airbox after the throttle, there are big issues with lag. If you imagine that every time the throttle is opened or closed the engine has to use all the air in the airbox first before the effect of the throttle is felt then you can see what I mean. Obviously maxiumum power and torque will increase slightly, due to the turbo, but at the expense of drivability. Because of the restrictor, max power is physically limited to around 80-90bhp and therefore torque becomes much more of a desirable characteristic. This is why there is an increasing move towards single cylinder endurance bike engines of a smaller capacity than the max 610cc. One paricular Honda engine we are looking at can be increased to 490cc with a power of maybe half the R6 engine but will have probably double the torque.
So...turbos are fun to do, and will give better bench results, but they're not that good in a FSAE car due to terrible throttle lag. There have been ways round it in the past, but the loop holes have been closed now. They included pourous airboxes and taking air from the crankcase breather last year
I think it was fairly obvious there was 'cheating' going on when some teams had engines producing more than the theoretical maximum!