There is a lot of missing details here.
To be able to be more specific and maybe give you solutions you need to give us the brand and model of the Laptop.
Quick Answer : Search for your computer brand and model with ubuntu/xubuntu.
Some generic answers can be made to your questions:
Why my WiFi is slower in Ubuntu 13.04 than windows 7?
This is weird, you should not have that kind of trouble with Ubuntu. Have you tried with the latest Ubuntu ? If not search for your trouble and specify the brand/model of your wifi adapter (you can have it usually by typing lspci on a terminal)
Why performance speed is slower than windows 7?
- If you are talking about the boot time: there is some hardware functions that are not yet well supported by Linux and others that are exclusive to Windows (Like some cache accelerator technology). However the lack of those technology impacts mainly only the boot time and not the performance.
- If you are talking about using it and it seems slower: Ubuntu has made a technological choice by preferring User Experience to Performance. Unity is a development made by Ubuntu to fulfill that purpose. If you are more focused on having performance, install XUbuntu instead of Ubuntu. It uses XFCE that is more optimized than Unity or Gnome 3.
Why Ubuntu > version 10.x is slow?
Maybe you'll find your answer in what I've already written.
You must also know that, by looking your CPU kind, you must have the latest version "13.04". Intel has changed a lot of things since that CPU model got out. If your computer is recent then you have the latest chipset of Intel witch changes a lot of things. One of them is the possibility to have two graphic cards : the Intel one and the amd or nvidia one. The Intel one is normally for common use and the other is for 3d. This choice is made by the drivers.
While the Intel graphic card is well supported, the amd or nvidia is still badly supported by open source drivers. You must look about how to install the proprietary drivers of your graphic card.
The 10.X part of your question can be explained with that before there weren't nvidia drivers with the ubuntu and then you used only the Intel GPU. Now you are using the Nvidia one but with slow drivers.
Why Ubuntu newer version consume more laptop battery energy? Is these problems are due to unity? I notice Gnome is faster than unity.
Your power consumption is surely due to the use of your amd/nvidia graphic card with Intel GPU behind. I don't remember the name for amd but take a look if you have optimus (nvidia) technology. If yes you must configure bumblebee
Unity and Gnome 3 have the goal to give good user experience by using your GPU most of the time. Try Xubuntu if you want something that is faster and with the same old interface. Unity and Gnome 3 will tend to use lot more power consumption (due to it's heavy graphic use)