Will this app run with 1 GB internal RAM?
No, the application won't run on computers with only 1 GB of RAM. According to the official system requirements provided by the developers, the software requires at least 2 GB of RAM and a computer with medium-high processing power to avoid lags and glitches.
Official requirements: http://support.bluestacks.com/hc/en-us/articles/204883885-BlueStacks-app-player-installation-requirements-
There were some versions modified to run on computer with 1 GB of RAM, but I don't recommend downloading packages modified by others as they might contain malware.