re shifter compatibility;
4700 RDs indeed have the same shift ratio as 11s 'road' mechs, so various things are possible here. However shimano 'road' 11s cassettes have a 3.74mm spacing and 10s cassettes have a 3.95mm spacing. This all means that if you use an 11s shifter with a 4700RD the mech will move 3.74mm per click not 3.95mm. Some folk would be happy with that, but if the adjustment is 'perfect' in the middle of a 10s cassette it'll be 0.2mm off per click away from the centre until the mech hits the limit screws; IME this is likely to be OK if you have to, but noticeably 'not perfect' otherwise.
There is also the issue of click spacing at the ends of the travel; 10s has 9 clicks, and clicks 2-8 produce an exact movement. Clicks 1 & 9 have longer cable pulls than normal to ensure that the RD is into the limit screws and that they determine the mech position in the highest and lowest gears. Thus if you use an 11s shifter you will be using a short pull (either click 2 or click 9) to access one of the extreme gears in a 10s setup and it may not work perfectly.
Re the brakes, ST-4700 has 'New Super SLR' brake cable pull which is considerably longer than older brakes used, with a lever mechanical advantage (MA) of about 2.5 or 2.75 or so . This will mean that without a travel agent or something, older brake calipers, centre pulls, cantis etc (which are deigned to use a lever MA of about 4:1) will be likely to feel 'wooden' and a bit feeble.
hth
cheers