I shall try to sort out your question for you at a basic level so you can find basic patterns.
1) Y means there, basically, but also means **it or that****.
It is used to replace a noun with **any verb that "takes" à:
aller à l'école (go to school) becomes y aller (go there). This is because of the à after aller. You have to learn which verbs "take" à.
Another example: croire à quelque chose: to believe (in) something. When the something is not present, that becomes y: Je n'y crois pas. And in this case, it means: it. I don't believe it. Getting the picture?
2) "On y va" is Let's go [there]; We're going [there]; Let's do it (in some circumstances). Remember the children's song: Sur le pont d'Avignon? L'on y danse, l'on y danse? That's a good example. The bridge is where people danse, or we danse, for example.
In French, the on pronoun (third person singular) is one, BUT it is often used in stead of nous or ils or even Let's. On parle trop vite en France. They speak too fast in France. or: We speak too fast in France. Whether it's WE or THEY or implied PEOPLE, as in the song, will depend on your context generally speaking.
3) Now, about Va-t-en: Here's another pattern, we can point out. Please bear with me through the weeds.
Some verbs do not take Y , they take DE. Sorry, you have to start to learn these as you go along.
And this one is also an idiom: to leave [a place] in French is s'en aller [to leave some place or to go away].
When the de [plus verb] is not present the EN essentially replaces it except with this idiom because for it, it must be present: s'en aller. The translation of EN can be SOME or IT but to have the meaning of leave or go away, the EN must be there. Je m'en vais d'ici maintenant: I'm leaving here now. I'm going away now [from here].
The imperative with the Tu is: Va-t-en !. Leave or Go Away! [imperative]
With vous, it's Allez-vous-en. Leave or Go Away [imperative, plural].
Tu is singular you and implies you know the person. Vous is plural you and/or polite you.
Now, all this you have to learn to conjugate:
Je m'en vais Nous nous en allons
Tu t'en va Vous vous en allez
Il s'en va Ils s'en vont
The good news here is that French basically only has one present for practical purposes: Je m'en vais d'ici à 16h. can be: I leave here [everyday} at 4 o'clock] OR I'm leaving here at 4 [today]. This is important for English speakers to grasp. And don't try to use en train de because that's too advanced at this point.
Other verbs take de: décider de faire quelque chose, to decide to do something. When the something is not stated, you use EN for it. Vouloir de [some thing, non-countable nouns mostly: du café, du sucre (masc.), de l'eau (fem. but starts with a vowel), de la tarte (fem). Décider de. There are many others.
Getting these right is important since food is so central to French life. Voulez-vous de la tarte? [Would you like some pie?]
Ce matin, j'ai décide de faire le travail. Becomes: Ce matin, j'en ai décide. [This morning I decided to do it.]
In France, the most important verb is (yep): manger and it "takes" de [or du or des or d']. So, to eat bread is manger du pain. And if the word bread ain't there, you get "en manger". Veux-tu en manger? [Do you want to eat some?]
Another example: Veux-tu du pain maintenant? Oui, j'en veux maintenant. [This is: Yes, I want some now.].
Your best bet is to try and learn the basic verbs in the basic tenses (present, passé composé, which is simple past in English]. You might start with aller, voir, and faire. They are all irregular. Then, go for three categories of regular groups of verbs. ending in ER (marcher, parler), IR (finir), and en ir-re-oir (prendre, partir, vouloir).
I suggest you watch French movies with the closed captions turned on in French. Children's books are good too. Try to repeat what you hear even if you do not understand it. In a couple of months after you do this, say, five to six hours a week, your understanding will soar.
Unfortunately, learning a language is a hard row to hoe and you're better off having a basic idea of patterns (i.e. grammar).
I merely have tried to give you a taste of what awaits you. Another common feature of French, is that French doesn't like too vowels together. So, that's why they write: Je n'y crois pas instead of: Je ne y crois pas. These are contracted forms. All the details are too hard to learn at once, but just knowing that will help you come to recognize this. Il n'y va pas. He is not going there. The ne followed by y becomes: n'y. To avoid two vowels together.
Finally, I think the Alliance Française has online courses. They present material in a graduated fashion, and make one or two points per lesson. I am sure they have online speech exercises. Good luck with your endeavors.