Scott S30 road bike 11speed with 10 speed compatibility
New 105 5800 crankset is compatible with older components, according to numerous posts in this thread.


Yes, you can use the same cassette.
Even if you use short cage rear derailleur now, it should have enough capacity for 28 teeth sprocket.
11 speed Shimano chains have the same internal width, so these should be compatible with older 10 speed systems. Given that you have limited budget, 10s might be a better choice.
Yes, that cable set will be fine.