Let's assume there is an emitter and a reciver. As the emitter is usually omni-directional, the reciver may get one direct wave and some reflected waves. Why does not these waves influence each other (they might even cancel themselves) and how it is solved the latency issue (a packet comes faster on direct wave than on reflected waves)?
Why does not these waves influence each other (they might even cancel themselves)
This absolutely happens. In fact, much of the strength of 802.11N is derived from its ability to use MIMO to take advantage of the multiple paths that the environment provides.
The latency issue is (partially) solved by using Automatic Gain Control (AGC).