What can i do to fight my case with two convictions and stop deportation proceedings.

If you are in proceedings you should absolutely hire an attorney and not rely on this forum

Based on my explanation above, will I be denied from citizenship ?

Please refer to the original posting

How long is it currently taking the process of sponsoring a Green Card through PERM Labor Certification?

Depending on your country of origin it can take anywhere from 1 year to at least 5 years.

Will I get into trouble if I Interned/Volunteered without authorization?

It will depend on your future employer, though I don't know why they would be upset

Is Disorderly conduct crime, offense or anything else? N-400 citizenship application.

You need to look at the precise code section

Do you know anything we can do?

Yes, speak to the recruiter about this issue.

H4 ead expiry

Both attorneys are absolutely correct on this issue.

Can I travel to my home country and come back to the US while applying for 'Change of Category' also simultaneously ?

Are you subject to the two year home residency requirement?

Are you talking about porting? Do you have an I-485 filed?

How many days can you take off between the job switch on H1-B? And what could be the downside of this?

It can cause problems - better to talk to the transfer company about having a new start date.