Does the asus z170 a includes wifi adapter, or do I have to buy separately?

No, it doesn't look like it comes with built-in wireless.

For best performance you should get an internal card.

Two modestly priced cards that are very well reviewed are the Gigabyte GC-WB867D-I and the TP-Link TL-WDN4800. Both run at around $40 and should provide you with great wifi connections.

**Special note, if you are running Windows 10 these might not work correctly for you.