Can I use nonbasic lands like {Kabira Crossroads} in standard even though it's from zendikar
I don't believe so. Type in the card in the card database and then check the legality section when the card comes up. It should tell you what format that card is legal in.
No.
Any card that's not being printed in any of the standard sets is not legal in standard. The rule is you can use a card from an older set if it is a reprint, like titans from m11 in standard since they are being printed in m12