Let’s start with the good news.
I don’t see the details of your uptrend. However, I am confident that an uptrend will help you a lot. This will help you with university admissions. More importantly, it will help you to be ready to do well once you get to university. This is a big deal. This is way more important than whether you get into a famous or highly ranked university for undergrad. Also, your SAT is quite good and suggests that you are likely to do well in university (particularly when combined with the hard work and improved study habits that are needed to create an uptrend).
However…
You can apply if you want to. I do not see either one happening for your undergraduate education. Your GPA is way low for these two schools. While your SAT is quite good, it is way below the median and somewhat below the 25th percentile for both Princeton and Harvard. Personally I would not even bother applying to either.
Also, I would not apply REA for another reason: You probably should want to apply EA to other universities where admissions is way more likely.
I think that NYU is similarly unlikely. Your chances there and at RIT might (?) partly depend upon how strong your uptrend is.
For engineering you should be looking for schools that are ABET accredited, and that are a good fit for you, and affordable, and where you can get accepted. They do not need to be famous or highly ranked.
I did not think that this was true for RIT. For the other three schools it is true if you can get accepted, but to me that seems unlikely.
As others have pointed out, there are some very good schools where you can get accepted and do very well. Your uptrend is huge and will most likely help you several ways, but probably not as an undergraduate student at Princeton, Harvard, or NYU.