How do i know if my motherboard will connect to my powersupply?

The 4 pin is for the CPU, so use the 4 pin plug on the PSU.

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Yes, all cpu's will need at least the 4-pin connector. The 8-pin variation is for supplemental power, which your motherboard won't need, and the end of the power cable will be keyed with shapes, so simply plug in the 4 that fit the 4-pin socket. As to your second question, the answer is yes, all power supplies come with cables for 4-pin cpu power (yours will come with an 8-pin, but again, you'll only need the 4 that fit) and 24-pin motherboard power.
 

Its not about the CPU.

Its about the mobo, what kind of connector it has. Some have 4pin some 8 pin.

And same it is with the PSU.

The 4 pin will work and power the 8 pin slot without any problem.