I 130 acknowledgement receipt?

Yes they do send a receipt within about two weeks

Can H1 holder in US be a Equity holder/Investor by taking certain percentage of share in the company ?

Absolutely you can invest in the company and as long as that is the end of the story it is permitted.

Given the case was dismissed, nothing. You do still have to report you were arrested in any dealings with immigration. For immigration purposes...

Any way around the H-1B cap?

No way around quota until congress does something. Only other possibilities are other visas you may qualify for. Cannot gauge that here.

The H1B LCA is good for max 3 years. The petition can be filed no more than six months before starting employment.

Can H1 Holders start a business and can he play a active role ?

No it is not possible under the H1B visa.

Could a green card holder obtain CCW in USA particularly in Maine State?

You have posted on wrong forum. That is a state law question.

Can a i-485 be denied, if I have been deported 29 years ago?

The answer depends on whether he revealed the deportation on his B-2 application.

Travelling during Conditional Green Card

The one extra year does not apply to your facts. Only if a waiver is involved and clearly not your facts. You can travel on your green card but...

White passport- reentry permit

He can apply for reentry but only after he has received the card.