Hmmm! So you can mount the new fan, but you need access to a 12 VDC supply. There do not appear to be any standard 4-pin Molex connectors inside your case, I presume. They are about ¾" wide with four holes in a straight line, and are commonly used for optical drives (also for old IDE HDD's you do not have). But your machine may have an optical unit with a SATA power connector on it - that is a PC card edge connector with 15 contacts in a straight line, same as the wide connector on your HDD.
Best idea I have is to trace the wires from your existing fans back to where they plug into the mobo. If that is a standard 3-pin or 4-pin fan post, you could use a Y-splitter to convert one port to two, and plug your new fan into that. If it happens to be a 4-pin mobo fan port, your 3-pin fan will always run at full speed. That may be OK for you - you seem to want lots of additional cooling anyway.
The only other option might be to splice into a known 12 VDC supply, like the appropriate wires leading into a SATA power connector. This is getting into cutting and splicing, not merely using adapters that plug in. If you do this, note common color coding: Red is +, Black is -. Look up the pinout details of connectors on the web. For SATA power connectors particularly, splicing into a wire might be better than trying to connect to contacts in the connector. I read that those connectors use THREE contacts for +12 VDC because 1 contact can't support the currents used by many devices.
On your new fan's case there should be two arrows: one points parallel to the fan shaft and indicates direction of air flow when the fan is wired correctly; the other is around the case and shows direction of fan blade turning. If you happen to reverse the fan's power connections by mistake, no big damage - the fan simply will turn backwards. So un-reverse the connections.