Is THHN and THWN wire rated for cable tray use? If not what wire should be used in cable tray in utility chase for apartment building?

Yes, you can use THHN/THWN wire in cable tray.

See :
http://www.southwire.com/support/THH...ifications.htm

It did occur to me, if you had to ask this question , you probably should be reviewing Article 392 of the NEC, as cable tray has special requirements for installing wire in cable tray, such as bundling feeder conductors, spacing between bundles, changes to ampacity of wire, etc.

Can 500mcm thhn be run in single conductor runs in a cable tray indoor for a service

Yes , see,

Quote:

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Originally Posted by tkrussell

Article 392 of the NEC, as cable tray has special requirements for installing wire in cable tray, such as bundling feeder conductors, spacing between bundles, changes to ampacity of wire, etc.

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Can THHN cabling be used for UPS batteries and in cable tray?

This application is from the battery disconnect to the battery terminals.

Yes.