I am about to download and install Visual C++ 2015 community. My computer only has 1Gb RAM. Is it sufficent?
You should be fine. Just idling (Not compiling, debugging, etc.) I am running it around 120MB for a single instance of VS. As for debugging I am running at around 200MB give or take for a smallish application.
Also, is it flexible enough to support C++11 and C++14?
You shouldn't have any troubles using C++11 and C++14 features with MSVC++ 2015. There is a few language features that aren't implemented for C++14* but I personally don't find that an issue. They also have quite a few features of C++17 implemented (And some Tech Specs like beta support for Modules).
I hear that modern C++ compliers nowadays comsume lots of computer memory these days. Is it true?
I have no idea, though I don't think it would really make that much of a difference... There really should be no reason to not use a modern compiler (Unless for some reason you need to target a specific compiler version).
I am about to download and install Visual C++ 2015 community
I really recommend you download the full ISO, not the webinstaller.
Mount the ISO with virtual drive software and do a custom install. Visual C++ is not installed when you do a default installation.
If you don't have virtual drive software you can get Virtual CloneDrive (it's free):
https://www.elby.ch/products/vcd.html
Why do I recommend the ISO? Easier to make changes to your VS installation without tying up your internet connection, and it installs so much quicker from start to finish with the ISO.