Please tell me what is the software which persons or companies use it to design the graphics of games (2D and/or 3D), is it 3DS Max? Is there any other software or any more simple software?
There's quite a huge list of softwares that can be used. The ones I'm listing here are the most popular ones, but you could do all your assets using paint and notepad
There is also XSI for animation and modeling, but it is less used.
No, Max is not used to design all game content. Some studios may use it to design some content, but there are many options for building content.
Some studios use Max, some use Maya, some use proprietary tools. Max and Maya are both 3D modelling programs, so some studios that do primarily 2D artwork probably use something like Photoshop (or again, something custom-written).