during the time period from when the receipt notices for AOS is received to the time when the conditional green card is issued on the basis of marraige to a USC I understand that one cannot leave the USA.
Once the conditional green card is issued , can one then leave the USA? if so for how long and under what conditions?
What are the residency requirements for this conditional green card to change into a permanent one?
how long does it take to get the US citizenship?
the case pertains to petition based on marraige to USC.

if you've never been illegal, you can get advance parole and travel

if you've been illegal, you have to wait for your card

The limits to travel if one has a conditional green card are the same as one who has a green card without conditions. You are free to travel as you wish. Any stays outside of the country over 6 months may involve the requirement for a re-entry permit. Any stays outside of the country of more than 2 years will likely mean abandonment of permanent residency. Any permanent move outside of the US (of any duration) can result in the determination that you have abandoned PR status. To remove conditions on the 2-yr green card you file an I-751 after 2 years (minus 90 days) from the time you were granted your PR status. Citizenship can be applied 3 years (minus 90 days) from the time your PR status was initially granted (assuming you meet all of the requirements).

sphy, i thought it was date of marriage instead of date PR status granted?

Conditional status starts on the day the green card is granted. It will be on the I-551 stamp (recommended for permanent residence on DD/MM/200X.) and on the card (permanent residence since DD/MM/200X.) Conditional status last for two years (DD/MM/200(X+2)) 90 days before the end of the conditional status, you file to have the conditions removed. DD/MM/200(X+2) minus 90 days.

Nope, the clock starts on the day PR status is granted, as Old Man has already indicated.

The only relevance of the date of marriage is for determining whether the applicant will receive a green card with conditions or not. If the marriage is 2 years or more at the time of PR status being granted then the applicant will receive PR status without conditions. But, as above, all folks with conditions attached to their green card start counting 2 years (minus 90 days) from the time conditional PR status was granted, regardless if they have been married one week or one year at the time they adjusted.