I'll give my two cents and I'm sure others will add theirs:

"What does a preamp contribute to a 2-channel system in terms of sound?"

In a perfect world a Preamp shouldn't contribute anything to the sound of the system but instead pass along the sound exactly as it exists on the source album/cd unpolluted.

"If I have two monoblocks powering my speakers, what is the job of the preamp in terms of amplification?"

The Preamps job in this configuration is to deliver the Analog (L/R channel signal) it has been fed from your source to each amplifier with enough voltage and as little noise as possible to drive the amps to their full output potential.

"How important is a preamp in terms of sound?"

It could be argued that it is one of the most important devices in your system as it controls the volume level and source selection features and it must do this as transparently and as true to the source as possible.

"Is it important to consider the synergy between preamp and the power amplifier?"

I feel that it is very important to consider this when choosing a Preamp but at the same time you don't want to pick a Preamp geared too specifically towards your current amplifiers unless you have no intention on replacing them. You don't want to have to replace your Preamp each time you decide to swap Amps. If you stick with a well measured and respected Preamp that is known to contribute as little as possible to the music then you would be well on your way to keeping the synergy

"Can one be tube and the other solid state?"

Yes, for sure. Many folks do this to balance out any sonic signatures that may exist between a Solid State and Tube component. Most will say that a tube device is more dark and liquid sounding and a solid state device is more bright or raw sounding. This of course can be a highly debated / heated topic though.

Good luck on your new journey 

What's supplying the source signal to your monos now? 

Typical cautions are to avoid a high impedance output pre amp with a power amp which has low input impedance.  The reverse usually isn't true as pre amps with low impedance outputs will often drive most loads.

In some cases a certain pre/power amp combination may have an audible affect, other times it may work to counter other system irregularities and, sometimes, any impedance mismatch won't be noticeable.  Other system synergy may have greater effects than close impedance matching, alone.