4-Pin Peripheral power cable to Fan 3 and 4 pin power cable: Conversion questions

You have found precisely the right solution. That adapter draws power for all its fans directly from the PSU via one Molex 4-pin output, which CAN supply that much power (more than 8 amps max draw at 12 VDC for 3 fans), unlike a mobo fan port. The adapter's extra female connector is a "standard" 4-pin fan connector that MUST go to a 4-pin fan port of the mobo operating in PWM Mode (the default mode for a 4-pin fan port). That connector does 2 things: (a) feeds to the mobo (via port Pin #3) the speed signal from ONE of its fans for monitoring; and, (b) gets from the fan port Pin #4 the PWM signal that can be safely shared by all 3 fans on the adapter to control their speeds.

You can use less than 3 fans on this adapter, of course. Just be sure that one of them is plugged into the adapter's male outlet with all 4 pins.

OP, I'm not clear how many of these fans you have, and where they are to be used. There are basically two fan cooling systems in a computer case, each controlled separately. The CPU_FAN port controls cooling of the CPU chip, based on the internal temperature of the CPU chip itself. Normally that requires one fan, although some systems use two either in parallel for a large liquid-cooling radiator, or in series in a push / pull fashion with fans on both sides of the CPU heatsink. Your Hyper 212 EVO unit can be used with either one fan or two (push / pull). However, I doubt it requires one or two of those Delta fans - one of the Hyper fans might well be enough, and two in push / pull fashion would give lots of CPU cooling. If you use two of those fans in a push/pull setup on the CPU heatsink, you have only one mobo CPU_FAN port to plug into. So you'd need a standard 4-pin fan splitter to connect those two to that single port, and that's OK if you're using that fan type which typically consumes about 0.3 amps per fan.

I suspect your plan is to use one or more of the high-power Delta fans for case ventilation. That job is controlled by the mobo's three CHA_FAN 4-pin ports, which base their control on temperature measured by a different sensor built into the mobo. In your case you'd only need to plug that special connector from that adapter into one of those CHA_FAN mobo ports for the two signals. That would work just fine. It even appears that those Delta fans are the same thickness as common case vent fans, so fitting them in should be no problem. IF you can, try for vibration-isolating fan mounting sleeves (usually rubber that go through the fan's mounting holes) - maybe they come with the fan or with your case.

Finally, a modest warning. Sometimes people stick their fingers into a running fan to stop it for a brief test. I note that users on the Newegg website say do NOT do this - the fan is turning MUCH faster than most with lots of power, and it will cut your finger!