Learn English – need not come vs don’t need to come

English is unique in that "come" and "go" do not relate as much to direction of travel as your perspective when you speak. Perspective is where you imagine you are when you are speaking. For example, suppose I'm talking to my friend on the phone:

I am leaving right now to come to your party.

I'm not at my friend's party, but I visualize that I am at the party with my friend. In a similar way:

Would you like to come to my friend's party with me?

Neither of us are at the party, but by using "come" instead of "go" it's an invitation that visualizes us both at the party. Of course I could also ask:

Would you like to go to my friend's party with me?

This is perfectly grammatical. The only difference is my perspective of us, here, moving toward the party together.

So the answer is all of your sentences are correct, and most of the time it doesn't really matter where I am when I say them. "I come to work", "I go to work" -- either way I don't have to be at home or at work to say these. It all depends on my perspective, whether I imagine myself already at home or already at work.

Keep in mind you have to use the perspective that makes sense in context. If my friend and I are thinking of a trip to Europe, I would say

Let's go to Europe.

and not

Let's come to Europe

However if I was talking to my friend in Europe I might say,

I want to come there to see you!

The difference is that, in the first case, there is no one in Europe whose perspective I relate to. In the second case I can put myself in my friend's shoes and see myself coming toward her. However, I can ask my friend in the US:

Do you want to come with me to Europe?

because I visualize that person with me as we move toward a location -- she's "coming along" with me.

It may sound confusing at first, but it does make sense once you get used to it.

TL;DR It's fine to use more than one in a sentence.

If you're looking to explain it, note that you have two different subjects for the two verbs: "the reason is" and "it is". That's a good hint that you have two separate verb phrases. The two verbs aren't really constraining each other in any way — they could even be in different tenses.

In fact, you could use as many different auxiliaries in one sentence as you like!

I haven't yet told you that the reason why I've studied English all these years has never been because I've been enjoying it, but because my wife has never been committed to learning French.

Clarification

Note that neither of those instances of "to be" is traditionally considered an auxiliary (but see the appendix below for a different opinion).

The usual auxiliary verbs in English are indeed to be and to have. However, those can both also serve as main verbs: they can carry the main meaning of a verb phrase, not tense/aspect information. That's what they're doing here.

How do you know when they're auxiliaries? Because they will be followed by another verb, to make a compound tense. For example, has followed by a past participle makes the present perfect:

He has called his parents once a week since he moved out.

And is followed by a past participle makes the present passive:

Our little church bell is tolled to mark every wedding in town.

You can see that in your sentence, the only other verbs are "study" and "binds". Neither of them is by "is", so they're not relevant for any compound tense. So you have to be as the main verb.

Appendix

^{As others have noted, some grammar systems call "be" an auxiliary no matter what. The one @P.E.Dant linked to below seems to be an example. But however you slice the cake, at some point you have to draw a distinction between "to be" as a support for another verb vs. as an independent item ("non-core auxiliary", for example?).}

^{It's worth nothing that in any case, "to be" behaves oddly for a verb in English, and so do similar words in many languages. Here it's a copula: it doesn't express an action like verbs are supposed to do, but declares an identity. You will see different grammar systems analyze it in very different ways.}

^{The good news is that no matter which analysis is correct, you're okay to use more than one in the same sentence!}