Smart home: circuit diagram

Do you think this conncetion is good, or would I need a capacitor or something else?

Does not appear you need a capacitor.

Whiles I cannot really tell much from a fritnutz diagram; not true schematics, I can see you are using a 9V square battery rated to give about 500mAh, through testing has shown those really only give 300mAh. What that tells me is in a few days you'll be back here with a topic that your project ran fine for 20, 30, 40, 50 minutes then suddenly the Uno restarts, the servos jitter, the relays click on and off, the motor fails to run, and a few other symptoms. We'll tell you that the square 9Volt batteries, don't use them. So start off right and get a different battery.

That you are using a servo, lets me know you'll need at least 1 amp of power delivery per hour. I'm sure the motor and supporting electronics will want about that much. The LED strip will consume quite a bit of current as well.