I have 1998 740i BMW that is overheating. 1) What are the warning signs of a bad water pump? 2) What are the warning signs of a blown head gasket? 3) What are the warning signs of bad timing?

you may have answered your own question .a blown head gasket will cause water to get in the oil therefore loss of water will cause it to overheat.driving under these conditions will cause more engine problems.

There are a number of possibilities:
1. Not enough anti-freeze in the cooling system. Anti-freeze not only protects against freezing, but also boil-over.
2. Defective thermostat. If it is stuck closed or partially so, it can cause overheating.
3. Clogged radiator.
4. Defective water pump.
5. Blown head gasket.

sounds like you have a head gasket gone bad. these cause overheating and the compression gases cause the air in the system and to boil out of the system. as such will cause the heater not to blow hot air, as steam will contain heat very long. the white smoke upon start up is a tell tale sign that the gasket has blown and needs replacement. have a head gasket test done. it could also be a cracked head or even a block, but head gaskets are a problem.

1- check and make sure the cooling fan is comming on 2-cooling fan relay is bad
3-or the temp sensor is bad
4-or blown head gasket or crack head

You have blown the head gasket. Also, you may have warped the head if it's aluminum which will happen due to ignoring the issue of overheating...which eventually caused the "blown head gasket". So, it sounds like you have 2 issues to resolve. 1) Why was it tending to overheat? Stuck thermostat, water pump issue or??? 2) Repairing the cylinder head or replacing it if warped badly, if your lucky it's just a blown head gasket. Allowing a overheating vehicle to be in service without solving that the overheating can lead to MANY other expensive problems.

Just because the headgasket was replaced doesn't mean its sealing.The head itself could be cracked or warped if the previous owner badly overheated it. Can you confirm if the shop who replaced the headgasket had the head checked for straightness and cracks?

Water in the oil means one of 3 things:

1) Cracked or warped cylinder head
2) Cracked engine block
3) Blown head gasket

Blown head gasket is the best you can hope for. And cracked or warped cylinder head is next most likely. A cracked engine block is least likely of the three. Have you noticed anything unusual, heard any noises? And has the car overheated really badly?

You need to read this article. It seems like there could be a blown head gasket on your BMW.
Anyways.. > how to diagnose an overheating engine.

you might have a blown head casket try due a pressure test on each cylinder and sometimes you can take a spark plug out 1 by 1 and just tap the ket so it cranks and see if water comes out of the cylinder

Several things can cause this overheating. Have you recently done a:
1. Check Hoses for Leaks
2. Check Radiator for Leaks --- Also, Change Radiator Cap ( can loose pressure there if
cap is bad)
3. Check Water Pump for Leaks. If Water Pump is bad, you will hear a loud noise from it
4 Complete Tune Up? Should be done at least 1x a Yr. Depending on how much you drive the Vehicle. Includes: Plugs, Plug Wires, Gas Filter, Air Breather Filter, PCV Valve, Adjust Timing,
Check Belts -- see if worn
5. Changed your Thermostat & Gasket and have the correct degree Thermostat in the Vehicle?
6.. Had your Radiator Rod and Cleaned out?
7. Temperture Sending Unit (located near Thermostat) could be bad
8. 02-Sensor (Generally located in the Exhaust Manifold - needs a socket with a space in it
to allow the Socket to fit over this top wire of the 0-2 Sensor )
9. Change oil and oil Filter.
10. Change Gas Tank Cap ---

Do all this yearly ( except the Radiator Rod & Clean ( do every 2-3 yrs), and you should not have
any over-heating nor stalling out, etc. and should pass emissions as well.