To me, it sounds like your mechanic is a parts fitter/helper and not a knowledgeable technician. Running in of a new engine is not related to vehicle speed, it's all to do with engine speed. If it was my car, I would keep engine revs below 3,000 for the first 1,000 km then use a good quality flushing agent then change the oil and filter. Don't let the engine idle for long periods. If the cylinder head was off, I would also flush, refill and bleed the cooling system as there could be traces of oil in it. After that, just drive normally.
The engine and airbag warning lights on indicates that there is a fault. The mechanic should have scanned for codes to see what the problems were and repaired then and reset, or just reset if no further repairs were required. Warning lights don't just appear without reason and when they are illuminated, it means there is a problem.