I'm using Easy CD-DA Extractor for urning audio CD-s. Mostly I have FLAC as source files. Now the question is: can I burn the FLAC or APE files directly to Audio CD or should I convert them to WAV first? Is it still lossless after FLAC to Audio CD?

Yes it will still be loseless after you burn it to an audio cd, if you use the proper write offset.

yes. standard CDDA is wave. If you dont convert them you will be able to play it only on players supporting flac/ape and there are not many I believe.

If you are burning Audio CD's (not data CD's), and your program can handle FLAC's, the file(s) will automatically be decompressed to standard PCM when it is burned to the CD. This is required to make a red book standard Audio CD.

http://en.wikipedia.org/wiki/Compact_disc

I'm sorry. Let me put the question around. I got two options:

1. to convert to .wav and then burn the wav files to audio CD
2. to burn audio CDdirectly from .flac, skipping the option 1

Is the outcome the same (in a sense of lossless)?

Also somebody mentioned 'proper write offset'. What's this?

The outcome will be the same if the program can decode FLAC.

A description of WAV:
http://en.wikipedia.org/wiki/Wav

WAV is a container format, most commonly holding PCM audio data. CD's contain PCM audio data. Your burning program has to decode FLAC files to PCM to burn them to CD. For that matter, FLAC's have to be decoded to PCM to be heard as well.

So either way you approach the problem, the audio that ends up on the CD is still PCM. Burn straight from FLAC if your program allows this, it will be easier on you and makes no difference to the end result.

As for the Write Offset, this article explains things nice and visually. If you cannot set this in your program, it will be a moot point anyways.
http://users.pandora.be/satcp/eacoffsets00.htm#-

P.S. I have no experience with Easy CD-DA Extractor, if you can't tell.