If the voltage drop across the LED's is something like 1.5V then 3.5V across the 1K resistor will draw 3.5 milliamps each or 87.5 total. You have close to 400 mA to spare with USB power probably closer to 900 mA to spare with 7V power.
I wouldn't expect any worries except possibly dim LEDs. Typically they use 20 mA each for full brightness. If you run them that bright the 25 LEDs alone will take 500 mA which is all that USB can supply for everything. Good thing you are running them on such low current.
kustom:
In case I'm going to need full brightness (which I probably won't) - can I power LEDs + those chips externally while controlling them via Arduino?
Yes.
If you supply unregulated 7v to the power jack (or Vin pin) the onboard regulator should be able to supply enough regulated 5V (on the +5V pin) to drive all the circuitry.
Alternatively, if you have a regulated 5V supply it can provide power to both the Arduino (on the +5V pin) and to the external chips.