Yes, quite massively, anything below GTX750 in Nvidia 7xx series is total crap

Yep, R7 265 is considered as an upgrade, minor one, it is a rebranded version of HD7850.

Depends on which part/component of your GPU is broken, if it is a minor one then it should be within the acceptable budget range, but I am just worried that nobody can quote you a reasonable price for the repair service since 650Ti is an old model, high chance that the components/parts of the card are already obsoleted

What's the main purpose of the rig? Gaming? Rendering? If gaming then you better focus more on the GPU instead of the CPU, GPU does help you by providing better and a more stable frame rates in games while CPU doesn't in most of the scenarios.

Yea quite huge the difference between 1050Ti and 1060 6GB, 1050Ti is around 65% of the performance of 1060 6GB, so you should expect to get around 40 FPS in games with 1050Ti if the 1060 6GB is able to output 60 FPS in the similar games.

For example,

i5 7500 + GTX1060 6GB = 60 FPS
i5 7600K + GTX1050Ti 4GB = 40 FPS

Clearly the first option is more preferred as it is able to output more frame rate (higher performance per price).

HP & Dell & Lenovo are OEM, you won't be able to see them in custom rig world except monitor and OEM PC

Intel Core i7 7700 - RM 1424
Gigabyte H270-HD3 - RM 519
G.SKill Aegis 16GB (8GB x 2) DDR4 2400MHz RAM - RM 560
Zotac GTX1050Ti 4GB GDDR5 Mini - RM 729
Intel 600P 256GB M.2 PCIe NVMe SSD - RM 448
WD Blue 1TB HDD - RM 219
Superflower Leadex Silver 550W - RM 359
Tecware Alpha - RM 219
Dell UltraSharp U2417H InfinityEdge - RM 1019
Logitech MK200 Wired Combo - RM 65

Total: RM 5561 (ETECH price inclusive of GST)

I picked a premium Dell UltraSharp monitor because PS is in the list, it comes with 99% sRGB coverage which is excellent for photo editing. To max out the budget, you may upgrade the GPU or monitor to 27" or 1440p model.

You are free to modify the build according to your own preferences