I have a Scott S30 bike currently running a shimano 105 2x10 speed 50-34 crankset, shimano 105 10 speed front shifter and 10 speed cassete and chain. I have a new crank that i want to install, the shimano 105 5800 53-39 but it is 11 speed. I'd like to know if i can make it work with the rest of the bike. I will change cassete and chain anyways because they already need replacement. So i have some questions:

Can i buy the same 10 speed cassette i used before?
I use a 12-25 cassete now, can i upgrade to a 11-28 one or does this require a special rear derailleur?
The chain can be the same 10 speed chain or should i buy a 11 speed one? I have read mixed opinions on this. Some say its fine with 10 speed other say its better with 11...
Are this good cables for my bike? I need to replace them but i can't spend much Bike24 - Shimano Road Shift Cable Set Standard

The chain and cassette have to match the rear derailleur and brifters, not the crank. The crank is the least important item for matching. If you can return the crank for a 10 speed one, that is what I would do. I wouldn't run what you are proposing, but you seem to be in a bind, so just try it. I think the rings might wear faster than normal.

There should be no problem running a 10 speed chain on a 11-speed crank, whatever that means. I'd be more concerned about the rear shifting suffering because of the 11-speed chain. Looks like you're good to go on the rear derailleur combined with the 11-28 tooth cassette. Buy the best Shimano cables you can, under bar-tape routing of shifter cables make quality cables all the more important.