Good question!  We do not have plans to change the El Nino/La Nina thresholds at this time.  As this document from the World Meteorological Organization indicates, most countries around the world use the same 0.5 deg. C threshold that we use.  Also, a World Climate Research Programme working group of scientists decided upon the 0.5 deg. C threshold for at least five consecutive seasons, and that became the basis for NOAA's official definition.  This persistence criterion is important because a few seasons in a row with a Nino 3.4 index above 0.5 deg. C or below -0.5 deg. C are usually (but not always) enough to see an ENSO atmospheric response.  This also helps to emphasize why we do not put too much weight in the Nino 3.4 sea surface temperature for a single month - we need evidence that the value will persist above the threshold. 

Your second question, if I understand it correctly, is a bit trickier to answer.  I will start by saying that ENSO depends on feedbacks between the atmosphere and ocean.  When the atmosphere is warmer, it is tougher to get an atmospheric response for a given sea surface temperature value, and so it might be useful to see how warm or cool the tropical atmosphere is for a given Nino 3.4 index value in order to see if an atmospheric response is more or less likely.  However, in the bigger picture, we also have to consider changes in the ocean, and the patterns of ocean warming can have a big impact on how ENSO will change in a warmer world.  The bottom line is that it's complicated.  We have discussed some of the climate change science and challenges here, here, here, and here.