What does it mean when a DA blocks a report? They trew it out?

That is not a common term, "blocked a report." What do you mean?

Can I request an appeal?

That is unlikely especially if the judge gave you the usual allocation

How long till trial from last court date?

There is no set time for trial. Your current lawyer is the best person to advise you about a plea. But if you have never been arrested before a...

What the charge for d felony

There is no standard time, but there is a statute of limitations.

Pending Protection Order- -NYC

If he does not show up to Family Court then the order may be granted without opposition. If he violates the order he could be arrested for...

Does this mean it's dismiised and sealed or no bcause I paid the fine for it

For the purposes of your question, yes. The fine is civil not criminal, as you pointed out.

Do i have to go

No, but it sounds like the police may come for you if you don't. If you do go to the station bring a defense attorney.

How can I get this misdemeanor off of my permanent record?

Is the case still pending or did you plead guilty or you convicted of petit larceny? Unfortunately in New York there's no such thing as expungement.

It shouldn't but you should consult with an immigration attorney. Best of luck.

What will occur?

Are you writing this in real time? Contemplating that in the future? If somebody burglarizes your home you have a right to defend yourself.