Which processor+Graphics card and network card is better for gaming, 3D design, multitasking, movies?

Talking about the 840 Yes for gaming it will do fine possibly, but also you do need a better card for 3d design. Have you looked in the 860m. It will give more than the performance you need and for a similar price. But you do need better than the 4600. Also have you considered 765m there harder to find but they are really good. Also where are you buying may I recommend a custom built cyberpowerpc I have bought from them many times and they are really high quality. Also I here PC specialist are good and more user friendly if you don't really no what you are doing. Now cpu wise I would recommend HQ. And finally I think that with cyberpower their is a scheme were you can get a free upgrade from an i7 4700mq and up to a 4800mq

"Is the 4th generation Intel® Core™ i7-4710HQ Quad Core Processor + Intel® HD Graphics 4600 better or
4th generation Intel® Core™ i7-4510U Dual Core Processor + 2GB/4GB NVIDIA GeForce 840M Graphics"

I think you should go for the 840m as it's clearly better than Intel HD Graphics 4600, and the GPU is usually the bottleneck and not the CPU

"Also, which is the best networking card and why?
802.11b/g/n WLAN [1x1]
-$30.00
802.11b/g/n WLAN and Bluetooth® [1x1]
-$20
Intel 802.11ac WLAN and Bluetooth® [1x1]"

The 1st and 2nd options are both the same but the second one will inclue bluetooth. Although the Intel 802.11ac WLAN and Bluetooth's model is not specified It should be better than the other two and provide a better experience specially if your router supports ac.

"For the processors and graphic cards, which is the best choice for gaming, 3D design, multitasking, movies? I multitask and game so I need a powerful processor with good graphics.
I know the first one is a better processor with worse graphics, but the second one is slower with better graphics. Which one is a better general option?"

The one that bundles 840m + i7-4510u

If you want a higher GPU as others are suggesting I believe you'll have to stretch about 200$ (I searched on google "hp 15t" and that laptop is about 800$?) Systems that bundle an 860m cost between 900$ and 1200$

Have you looked into custom build laptops?