If our resume doesn't specify the time horizon for each level we worked at our current company, can the recruiter or hiring manager ask how long we have been at a particular level and when we were last promoted? Can they also ask about your recent performance rating?
If recruiter or hiring manager can ask the question, what's the best way to answer?
If the promotion happened very recently, will we be at the risk of getting down-leveled?
On the other end, if we stayed at the current level for a long time, would they perceive it as a negative sign?
Yes, they are free to ask those questions. Likewise, you are free to answer them by not giving them an answer. You can tell them they can let the results of your interview speak for itself & you can provide references if it's needed.
If the promotion happened very recently, will we be at the risk of getting down-leveled?
I've mainly seen technical interview performance used to inform what level an engineer should join a company at. The difference between a mid level and senior engineer is how well they do at the system design portion of the technical interview.
It's possible that it could be used to downlevel you at companies that are known to be more stingy when it comes to setting the initial level of an engineer.
The best way to sidestep all of this is to get as many offers as possible so you have more leverage on coming in at a certain level.