Hello, I hope the following assists you.
From the description you give the engine is cutting out when you press the clutch and restarts when the clutch is released in effect been bump started, the lights come on when the engine stops and the steering is heavy because when the engine stops the power steering pump isn't turning any more.
If this didn't happen previous to the timing belt replacement then it would seem as though it's due to the work the garage have done.
You can check for any pipes that may have been left off the engine or damaged especially the breather pipe at the back of the inlet manifold, also check the electrical connectors to the camshaft sensor and ignition coil, check the HT leads for any sign of electrical arcing on the inside where they connect to the spark plugs as all these are disturbed when the timing belt is replaced.
Unfortunately the only other option is to make sure the valve timing is correct which means removing the valve cover so this should be a last resort but as I mentioned earlier if the engine ran fine before the belt replacement then I would suspect something associated with the work carried out.
Let me know if you have more questions regarding this and I'll reply as soon as I'm able to.