Can I install apps to different devices from one device? I am wondering if there is a way to install and open apps on different devices I am signed onto from one device.
I think what you are looking for is Apps Syncing across multiple devices. AFAIK, there is no native way to directly do this. You would need to have something like what this App Sync app is promoting.

 Disclaimer: I am not associated with the app's company or developers in any way. I just did a quick search and their app was the first one to show up. 

IMHO, I think apps syncing would is convenient, but may result to some crashes, since there is a chance where your devices each are using a different Android OS version, different specs, and last but not the least is app device specific compatibility (e.g. Tablet-only apps).