Dota 2, CS:GO (and other heavy single core application or single threaded application) runs faster on a CPU with higher core clock speed, i.e. i3 7100's 3.9GHz will beat i5 7400's 3.5GHz in those games, but when it comes with multicore or multithreaded application, i5 7400 will lead once again.

Rise of the Tomb Raider favors Nvidia GPU, even in DX12 mode, with the recent driver update (378.78), performance is boosted even more for this games in DX12 mode (they claim to have 20%+ for 10 series GPU).

Intel Core i5 7400 - RM 835
Asus H110I-PLUS - RM 380
G.SKill Aegis 8GB DDR4 2133MHz RAM - RM 289
Gigabyte RX470 4GB GDDR5 G1 Gaming - RM 989 <Cheapest GTX1060 3GB is 1.2k at Idealtech so I will have to use RX470 to replace it> 
WD Blue 1TB HDD - RM 219
FSP Hexa+ 550W - RM 219
Shark Zone C10 - RM 199

Total: RM 3130 (Idealtech price inclusive of GST)

Another build with GTX1060 3GB from ETECH:

Intel Core i5 7400 - RM 854
ASRock H110M-ITX - RM 283
G.SKill Aegis 8GB DDR4 2133MHz RAM - RM 255
Zotac GTX1060 3GB GDDR5 Mini - RM 989
WD Blue 1TB HDD - RM 219
FSP Hexa+ 550W - RM 195
CM Elite 110 - RM 158

Total: RM 2953 (ETECH price inclusive of GST)

It is hard to predict what is going to happen in the PC gaming industry in 5 years time, if DX12 and Vulkan are able to take over DX11/OpenCL as the main graphics API successfully in 5 years time then according to the current card performance, AMD will take the lead again, their Polaris GPUs are showing better performance than Nvidia's similar offering at the moment in few DX12/Vulkan titles.

If you want something more stable (in terms of current games support and frame rates) then Nvidia is more preferred as they are having a very solid DX11 driver support base now.

Both brands are equally good actually 

i5 is within the budget range, i7 & Ryzen are out of reach.

Used unit price for i3 7100 should be around RM 400+/-, but bear in mind that Kaby Lake i3 is facing a strong competition with an entry level G4560 which is having similar core configuration as i3 (2C4T), value might drop further.

It depends on the mobo that you already have. Given that your friend already has an i3-7100 (Kabylake), he could consider getting an i5-6xxx (Skylake). Unfortunately, that motherboard cannot be used with older generation of CPUs

1st gen bruh

The R3 series will be equivalent to i5, to compete with i3. It is possible to get both the processor and motherboard under 1K, considering AM4 boards are quite cheap.

Sadly, it hasn't arrived yet. Wait for the announcement.

There will be. The cheaper A320 chipset will come soon.

If no radiator or anything that can block the airflow (front panel) then no need to go for SP, AF is more efficient in this case.

2 AF120 for front panel, 1 AF120 on top and 1 AF120 for rear panel. Or just get 2 AF120 without buying 4 new AF120 at the same time since the case comes with 2 120mm casing fans already.