I'm at my wits end about this:

1) Why has it become so common for Eastern Catholics to claims they do not have to accept any Church decision after the Second Council of Nicaea?

2) If the filioque is dogmatic, why are they allowed to say the Creed without it? I've only ever heard of this concession being used to justify point #1.

Does anyone know where to point Eastern Catholics to, what source they will accept, that says they are in fact obliged to believe the One Catholic faith the same as any Roman is?

2) is easy to answer: Because they never have. Every true dogmatic statement doesn't have to be in the Creed.

1) generates a lot of heat and smoke and very little light, so I'm not going to try.

The same goes for the unnumbered third question.

The Syro Malabar Church uses the filioque on the creed.

To 1. There is/was in some quarters a mutual hatred, a desire to be different and feeling of superiority.
There is the stereotype of a Latin being over-curious, legalistic and lacking a sense of mystery.
(OTOH there are also some pro-Latinisation (or rather, OF-inspired simplicity) camps as well.
To 3. Do they accept Vatican II? If so, try quoting from it and from post conciliar Magisterium on the unity of faith and the unity of the Church.

I suppose 2) was mostly a question of prudence of said decision.

I am actually anxious about the fate of these people's souls I really don't understand why people say they are Catholic and preach another religion.

They are Catholic. Why would they call themselves anything else?

If they deny the filioque, the authority of the Pope, the authority of all ecumenical councils from Fourth Council of Constantinople to Vatican II, purgatory, the immaculate conception, etc.

In what sense are they Catholic? Obviously there, of course, are many many good Catholics in the Eastern rites, but there is a growing error amoung some of the pople (lay and clerical) that they are not bounded to hold the Catholic faith.

The reason this is in the Apologetic sub-forum is because it is an apologetic issue. How does one address this issue?

I don't have any answers for you, these just aren't issues I have read on very much.