Can I transfer my iPhoto pictures (and Photos) to new iMac?

Copy/transfer your iPhoto library to your new Mac, launch the Photos app with the Option key held down and open your iPhoto library. It will be migrated to the new format in a separate library.

If you're still running iPhoto on your old Mac I'd launch the library with the Option and Command keys held down and run the following two "repairs" on the library before migrating to Photos:

1 - Repair Permissions

2 - Rebuild Thumbnails

That will help assure that you have a smooth and full migration from iPhoto to Photos.

You will need to convert your iPhoto Library into a Photos Library. iPhoto won't run on a new computer.