Do you need to replace the timing belt when you change a water pump for a 1998 mercury mystique v6?

Changing the Timing Belt in Mercury Mystique

http://www.ehow.com/how_8217220_install-2000-ford-contour-v6.html
couldn't find your exact model, but this is the procedure for that motor.

You can reuse it. But you need to find out why it was thrown off. Check all the pullies by grabbing them and checking for side to side movement, With the exception of the power steering pump pulley (which has some in and out play) they all should have no play. Just turn in nice smooth circles. Sorry I don't have the diagram, but there should be one under the hood. Sometimes on the bottom of the hood.

how do i get the bottom timing pulleys off so i can get the water pump out of my 1996 mercury MISTAKE!!! OH I mean Mystigue

Here is a link to a series of videos which will walk you thru the entire process...

http://www.wonderhowto.com/how-to/video/how-to-replace-a-water-pump-in-a-vehicle-102464/

parts store has a manual for you for about $20 that answers both those questions

check for a bad head gasket

For the 1999 Mercury Mystique Water Pump Belt on 2.5L V6 Engine:

Probable Causes: Belt: worn out, started slipping. Overheating caused by failure of Belt. Lost antifreeze: caused by failure of belt, not turning Water Pump Pulley, not circulating anitfreeze, which resulted in overheating.

Click on the following free direct Link. It has the Serpentine & Drive Belt Diagrams and Tensioners for your 2.5L Engine.
Scroll down the Page (about 1/3rd down) to Diagram #G99H08189, it shows the specific Water Pump Belt.
Note the Tensioner.
http://www.2carpros.com/car_repair_information/year/1999/make/mercury/model/mystique/1999_mercury_mystique_drive_belt_routing_diagram.htm

Let me know if this helped, or if you have additional information or questions. Feel Free to contact me at FixYa.Com!

My sincere apologies for the delayed response.
I am personally going back to answer your unanswered questions.
I have only been a free contributor to this site for the past 4-months.

I do not know if you still need this information, but I am going ahead and answering it anyway. You may want to Print the Diagrams for future use.

CLICK on the following LINK. It has the Timing Belt Diagrams you will need.

If you would: Before Clicking: Let me know if this helped you, or if you have any additional information or questions. Feel Free to contact me at FixYa.com!

Again my apologies...
http://www.2carpros.com/car_repair_information/year/1998/make/mercury/model/mystique/1998_mercury_mystique_timing_belt_diagram_marks.htm

I i were you i would check the ignition. it sounds like you are only connecting some of the time. And yes it is very normal to hear the fuel pump kick on when you turn the key to the on position.