Electronic – arduino – Transient Current Effects from Independent Charging Circuit

It's hard to tell from that picture, but it looks like you have maybe two wires from the arduino going to the breadboard, and two wires going from the breadboard to that thing on the left. Assuming the thing on the left is the remote control, and that, from what you said shorting its two wires together turns it on, then it's very possible to have, as you say, a transistor that's normally open.

The usual thing would be to use a cheap NPN transistor like a 2n2222 or 2n3904. The collector of the NPN would go to the more positive of the two leads from the remote. The emitter would go to the other remote lead. (Use a DVM to be sure which is which, you can't always count on insulation color!) To ensure that the NPN passes no current when no input is connected, you can put a 50K or 100K resistor across the NPN's emitter and base leads. Then, to get input from the arduino, connect the arduino's ground to the NPN's emitter, and connect the arduino control signal you want to use to the NPN's base through a resistor in the range of 1K to 2K ohms.

A circuit like that should not activate the remote when you disconnect the arduino.

Your motor that you linked to is a 4.5V 190~250 mA (No Load) motor. At 9v, the current probably increases. You are overdriving it by 200%. And any load/weight will cause it to increase in current requirements as well. Stall current is probably 10x that at least.

You are missing the protection diode across the motor, that can easily kill the transistor.

The Transistor you are using is a 100mA standard, 200mA Absolute Maximum. One of those motors by itself without any load, can easily kill that transistor.

The base resistor is calculated as (Base Voltage - Base-Emmiter Voltage) / Current required. Base Voltage is the Arduino pin, so 5v, Vbe depends on the collector current which is 200 mA here, so typically 1V. Current required is calculated as Collector Current (200mA) / Hfe (From datasheet, 10~30). On the safe side, lets go with 10, so 200 / 10 = 20mA needed at the base.

(5V - 1V) / 20mA or 4V / 0.02A = 200Ω resistor. A 1kΩ resistor would only allow 4mA at the base, which times the Hfe of 10, would only allow 40mA at the collector, probably no where enough to tun on the motor.

TLDR: You need the protection diode, your 9v power source is too high, and your transistor is too weak for the motor you are using. And you need a bigger resistor at the base because the motor requires more current then you are figuring. A common 2n2222 transistor with a 470Ω resistor would do much better.

Edit: Not making the pin an output also puts a damper on things. Answer, Arduino pins default to input.