Can an appeal now file upon the dismissal of complaint, although decision not yet issued on motion under CPLR 1201 & CPLR1202?

It sounds like you should meet with an attorney assuming you don't have one now

Early probation termination

Not that I would recommend it but a VOP and jail will result in termination of probation

Lady friend informs me that future ex-husband may have linked me to e-mail addresses dealing in porn/child porn.

Consult with an attorney as soon as posible

Can my landlord evict me over non payment of a water bill in her name?

Not as a nonpayment petition, yes if holdover

Can an individual case be sealed as part of a settlement agreement? If so, would the case not be able to be used by others?

I believe the answer to your question is yes, others could not use it ...

My son was charged with criminal possession of a firearm 2nd and 3rd degree

If the gun was not his theoretically a very good attorney will get. It dismissed. You should consult a lawyer in person immediately

What type of goverment agecies can see the charges if they do the background checks

Yes they do. Tell the truth on work applications but get a certificate of disposition in case you need to explain what happened

The answer depends on all the facts. he should immediately find a lawyer that offers a free initial case evaluation.

How much time is a person who comitted third degree burglary looking at?

Max 3 to 7, but it can be a lot lower depending on the facts

Can I put a restraining order on an older sibling who molested me 10+ years ago?

Yes go to the DA , Short of that you can try to get an order of protection from family court . Consult with an attorney with all the relevant facts