The new background is actually fleshed out in the Black Library book 'Hammer & Anvil', it may appear to be primarily about Sisters of Battle but it includes lots of details about the functioning of the tomb complexes and their inhabitants under the new style. The book is good and it has definitely softend my attitude towards the new stuff.
If you're enthusiastic about the new stuff definitely look at reading it, there's no need to read the precursor 'Faith & Fire' which is also good but has nothing to do with Necrons. I'll try to give some of the background insights here without giving too much of the book away.
Portals do still exist exactly as per the old style rules, and do still have access to ground based Tomb Complexes, they may be all but abandoned for nearby more functional facilities but the portals inside can still be activated remotely by other portals & Monoliths.
Phase out still exists on the battlefield scale, transporting severely damaged units back to the Tomb Complex of their origin/dynasty for repair or if the worst should happen back to the next nearest Tomb complex, which I believe may involve a change of ownership for low tier Necrons(this was heavily implied).
The Dolmen gate is actually something very special/rare, not all Tombworlds/Dynastys have access to one. It's a dimensional gateway used to give Necron forces access to nearby warp tunnels. I'll quote a couple of lines from the book here:
'The dolmen bores down into the matrix of the universe, the grid of line and power that underpins all things'
'The eldar have a name for that network, they call it "the webway".'
The very act of use corrodes/destroys the material of the Dolmen gate itself taking years of maintenance/repair to keep it working.
The new transports choices e.t.c. all seem to be there to provide options to the individual lord in command. He may, for instance, feel a monolith is a waste or overkill preferring to use ghost arks as transport and using other devices for heavy firepower e.g. the triarch stalker, doomsday ark, scythes. Basically he may be feeling snobby and using a Monolith to destroy an army of primitive upstarts would therefor be seen as beneath him.
I could go on but we're heading for 'too long didn't read' territory here...