How can a child of 17 years obtain his/her green card if his parents don't have it? Is there way to get it?

Your facts do not suggest that the child could.

I am waiting my ead renewal under my L2 visa, it will expire in 3 weeks, is there a way to work while waiting the renewal ?

yes, 180 days.

Is veteran affairs in houston "Michael E debakey" considered cap or non cap excempt for H1 visa

If they want to petition for your H1B visa, they will definitely know whether they are CAP exempt or not.

Getting married with the US citizen

You can seek waiver here but filing a waiver application does not provide you with the permission to stay. At the same time, you cannot apply for...

Getting married with the US citizen

You should talk to an immigration lawyer before the problems start piling up on you.

As one very good attorney I know always say - why don't you start by asking this question of your previous employer's attorney?

For citizenship purposes, what matters the most; what person has been arrested for or what person plead guilty to?

the latter.

Do I need to fill out form I-864 if my husband (who I'm applying for), is the only household income earner?

Yes.

My husband has criminal record and i want to apply for residency -> citizenship.

No.

Can I Get My Fiancé A Permit To Get Married in The U.S?

Yes, file for a fiance visa for him and he will be able to come and marry you here, in the USA.