I think your memory is deceiving you. 3.5 classes had more in common with 3.0 classes than Essentials builds have in common with 'classic' builds.
Really? I just played a Mage last night and someone commented off-hand that it was an Essentials class. I replied, "Oh, I didn't realise."
No you can't. A Slayer is not a PHB Fighter. So you can't freely pick powers between them any more than you can freely pick powers between Paladin and Fighter.
No offence guys but this is seriously showcasing your ignorance on the subject. The Character Builder has an option, "Show All", in every Essentials build which allows you to pick any power from the list for that class. A Fighter, therefore, is still a Fighter, no matter what it's otherwise called. In essence, all the Essential's classes are, are different builds within the same class. They're more 'sub-classes' than classes unto themselves.Before Essentials builds were entirely optional and you could mix and match powers in whatever way you wanted. You can't play an Essentials class without using an Essentials build and you cannot freely pick powers from classic builds and Essential builds.