Simple question, probably a simple answer. ;(
Is there a way to run PowerShell on my Windows Phone?
If not, is there another way to get to a legit console/terminal? Right now I have "Console WP8 Lite", which is clearly only an emulator. My phone isn't rooted right now, but I'd be interested to know if rooting would give me access to something like that.
The answer is No. You cannot run a Powershell in winodws mobile. Not until Microsoft implements it. I suggest you to upvote the feedback in the Feedback Hub.
What about 3rd party apps?
Third party apps, particularly the ones distributed via store cannot bring the full functionality of Powershell due the limiations that are there for security of the OS.
My phone isn't rooted right now, but I'd be interested to know if rooting would give me access to something like that.
There is no rooting Windows 10 mobile. You can hack into Windows registry to make changes to the OS. Hacking into the registry is not Rooting. You can edit the registry but you cannot have Powershell on Windows mobile.
Update:
Upon seeing CBHacking's answer I think it may be possible to read run scripts, read root directories, etc... It is not easy as rooting an Android but if you are ok with such things you could give it a try.
There's a basic shell program (which supports CMD-like commands, though it isn't actually running CMD) available on XDA-Devs here. It's an old version (1.5 years) and I should bug the dev about updating it, but it provides some ability to browse the file system and registry. You have to connect to it using a Telnet-like protocol (PuTTY works).
It can run EXEs, though they'll only have the same permissions as the app itself (not much, unless you elevate it by hijacking a more-privileged chamber or launching it as a Windows Service using a rooting hack, such as WP Internals). You can get a number of EXEs that will run (unmodified) on WP8.x/W10M by extracting them from the UpdateOS.wim file on the phone. Notably, this includes CMD.EXE (the real deal, make sure you also grab its .MUI file from the appropriate region directory like en-us), TELNETD.EXE (a basic Telnet server, syntax is telnetd <program> [port] so you could use telnetd cmd.exe or telnetd cmd.exe 22222), and FTPD.EXE (a basic file transfer protocol server, you can optionally specify a folder to root the FTP access in). I've seen copies of other real Microsoft EXEs, like REG.EXE, NETSH.EXE, BCDEDIT.EXE, SC.EXE, etc. but I do not now remember where I found them and they aren't on my current PC (and they mostly require elevated privileges to be of any use, anyhow).
Note that this isn't going to actually root the phone in any way by itself, it's just another way to access the data on it (including some data not normally visible). Another way to do this is to use an app such as the Native Access Web Server, which gives (partial, and mostly read-only) access to the file system and registry via a web browser.
Note that none of these tools I've linked have any authentication or encryption; don't use them on untrusted networks unless you want to risk total strangers connecting to your phone. You will have to use WiFi; cellular blocks incoming connections and loopback is blocked by the OS security model.
Given that you are running Windows 10, you can actually run T-Shell from your host computer and connect to your device.
I have only done this on non-retail devices. Download and install WDK 10: https://developer.microsoft.com/en-us/windows/hardware/windows-driver-kit
By having the device connected via USB cable you can connect to the device via open-device 127.0.0.1.
