Would it be possible to upgrade the CPU, RAM and GPU in this PC

Solution
Your link seems to show photos of two graphics cards in sli of GTX1070 class or higher needing a 6 and 8 pin connector each, coming from a proprietary psu. GTX1080ti perhaps?
I doubt that is what you actually have, despite the gtx1060 in amazon title.

Regardless, you need to check out the capability of your psu which may be proprietary and not easily changed.
A typical GTX1080 will need an 8 pin power connector that will come on a psu of >500w.
No telling what a GTX1180 or whatever it is called will bring.
See if you have that.
Replacing the i5-8400 with a i5-8700 should be reasonable.
Check with alienware on that.

Upping ram, you should plan on a complete replacement since the photos show all 4 ram slots already populated...
Your link seems to show photos of two graphics cards in sli of GTX1070 class or higher needing a 6 and 8 pin connector each, coming from a proprietary psu. GTX1080ti perhaps?
I doubt that is what you actually have, despite the gtx1060 in amazon title.

Regardless, you need to check out the capability of your psu which may be proprietary and not easily changed.
A typical GTX1080 will need an 8 pin power connector that will come on a psu of >500w.
No telling what a GTX1180 or whatever it is called will bring.
See if you have that.
Replacing the i5-8400 with a i5-8700 should be reasonable.
Check with alienware on that.

Upping ram, you should plan on a complete replacement since the photos show all 4 ram slots already populated.

Replacing a HDD with a sshd should be reasonable.
Adding a ssd is probably reasonable if you can find a place to put one.

All in all, though, you should be much better off building anew and selling the old as a complete kit.
 
Solution
i would say open the case and check

1. see what kind of dimm slot you have available.
then you can decide which form factor to buy

2.measure the physical size of your psu (Dimensions of an ATX power supply are 150 mm width, 86 mm height, and typically 140 mm depth, )
meaning you can swap out psu to power the size.

3.check the number of sata ports and and drive size, so you will know what form factor to get.

4. measure the space inside the case to know the maximum length height width, that you can fit gpu.

5. cpu will fit for sure, but 8700k maybe too power hungry, try 8700