What can I do in this vented crawlspace to keep the room above warmer?
It is a good idea to seal any apertures between the crawlspace and the main house.  If you have to rely on caulk and spray foam you're probably in a situation where the house has some weird structural problems - that is, you should not have giant gaps between the crawlspace and the floor above in any normal construction regimen.

It is not a good idea to seal off the crawlspace, ventilation is not only a good idea but it's required by code in locations where crawlspaces are an accepted norm (note that in places where winters are exceptionally cold the norm is finished and unfinished basements, not crawlspaces).  The fact that you have had mold in the crawlspace is actually an indication that you might need MORE ventilation not less.

A proper insulation/vapor barrier installation at the level of the floor joists should solve any draft problems.  Also, looking at your photos I would recommend that you insulate your ductwork/boots/wyes per local code.

So to reiterate, please do insulate and install a vapor barrier!  Do not seal off the ventilation for the crawlspace - indeed look into your local code to see if you have enough ventilation.

As a side note - any issues of moisture (and therefore mold) in the crawlspace need to be addressed.  Possible sources of moisture include but are not limited to:  leaky plumbing supply or waste lines, inadequate drainage system at the perimeter of the house (undersized gutters/downspouts, poor grading, no storm drain, etc.), and a possible high water table.

Good luck staying warm this winter!