Can we use "via" and "through" with alive things in the meaning of "with the help of"? For example:
These cacti were gotten by me [via/through] my dad. But for his help, I wouldn't have gotten them ever.
If you want to say "with the help of", I'd just say "with the help of". "with the help of" can mean that whoever helped you did everything and you did nothing, or something in between: whoever helped you did some and you did some too. Or it could mean multiple people helped you and they each did some of the work and you didn't do any of it. i.e. "with the help of" has room for different meanings in how much something was of help.
"via" and "through" are more about the method by which something was done, and can sometimes carry a meaning of physical route. But it would be a strange thing to say "I did this 50% via X" or "I did this 50% through X"- even if that were true in some sense. At least- I have never heard someone use such a phrase, or used such a phrase myself. The physical route senses of the words can be used in contexts like "I drove here via this route" or "Can you pass this on to Mark through Matthew?" (meaning a request for someone to pass something to Matthew and instruct Matthew to pass it on to Mark).
Sure, in colloquial English people use both "via" and "through" to indicate an intermediary who helps them do or realize something (it often involves relaying information).
The only place where it is natural in English to use the Latin “via” is in bus or train timetables, e.g. “This train goes to London via Birmingham”.
Everywhere else use through or some other form of words. Via is the sort of pretentious term used by people trying to sound educated. They don’t and they aren’t. (And if you insist on via, change the informal dad to father.)
As for the rest of the sentence, it is stylistically weak using the passive. Much better to write a direct sentence, e.g.
My dad got me these cacti. I would never have managed to get them without his help.
But in general you can use through in sentences like
I got this genuine thingamy through someone I know at work.