Hard to diagnose without more information, but it does seem that you continued to drive it when it had problems. It is worth fixing problems when they happen on these vehicles, as you avoid consequential damage.

Shaking on startup can be fuel related, control system/sensor related, or ignition related. Low coolant generally means, well, low coolant. That can be anything from a leaking expansion tank (reservoir) to something internal to the engine. SES light is generally emissions control related, but it can be a consequence of another problem.

Let us know what the shop says.

__________________
2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue