In Europe, is it possible that Transition Altitude and Transition Level are equal, that is, TA=8000 ft and TL=FL080? In that scenario, at 8000 feet, what pressure (QNH or QNE) should be set in the altimeter? Is it possible that Transition Altitude is higher than Transition Level, e.g. TA=10,000 ft and TL= FL090? If the above scenarios are not possible, is there some minimum altitude of the transition layer that must always be assured?
Both situations you describe are theoretically possible. Saying that 8000 FT is "equal" to FL80 is a false assumption. Only in one very specific situation would that be true: when the QNH is 1013. Whenever the QNH is different than 1013, 8000 FT and FL80 would be two physically different levels.
In Europe, the TA and the TRL must always be separated by at least 1000 FT1. The distance between TA and TRL is called the Transition Layer. The common way to handle this is to have a fixed TA (often 5000 FT) and a TRL that varies, depending on the QNH, so that the Transition Layer is always between 1000 FT and 1500 FT "thick".
What this means is that on days with a low QNH, the TRL will have to be "higher" (numerically, not physically) and vice versa on days with a high QNH.
Counterintuitively, if the QNH is 1047 hPa or higher, 8000 FT and FL80 are separated by 1000 FT, which means that if the TA is 8000 FT, the TRL can be FL80. Two aircraft passing each other, one at 8000 FT (QNH 1047) and one at FL80 (QNE, 1013 hPa) would be separated by 1000 FT. It is, theoretically, possible to have a TRL that is "lower" than the TA (for example TA 8000 FT and TRL FL75) while the TRL is still physically 1000 FT above TA, but that would require an unrealistically high pressure.
Similarily, when the QNH is low, the TRL has to be "higher" to ensure separation. If the QNH is 1010, 5000 FT and FL60 are not separated by 1000 FT (the actual separation would be roughly 900 FT), so in that case the TRL would have to be FL65.
I work at an airport with a fixed TA of 3000 FT. The TRL is continuously updated based on the QNH, and typically lies in the range of FL35 at the lowest and FL50 at the highest. But, the actual distance between 3000 FT and TRL will always be between 1000 FT and 1500 FT.
The TA and TL will always be at least 1000ft apart to ensure that aircraft flying at each will always be properly separated.
The TA will be a fixed value to ensure terrain and obstacle clearance, while the TL will be the lowest reasonable value that provides this minimum vertical separation above the TA. However, “reasonable” includes not having any possible numerical ambiguity.
So, if your TA is 8000ft, then the lowest possible TL is FL085. Depending on the QNH, though, the TL may be higher.