Is there any alternative voice assistant?
No. There are other apps on the Store that are "voice assistants", but none of them have the ability to link deeply enough with the OS to actually do any good.
I basically need it to take notes...
Well I'm not 100% sure on this, but I think you can still access Reminders offline, if that's what you're wanting. Otherwise you should be using OneNote or something similar.
The rest of the things that you mention are only available online, so the short answer to your question is: No.
There are a few things Cortana can do offline such as calling, texting or starting an app, but in general she's made to work online, and taking her offline would defeat the whole purpose.