Hi Mary,
First, you won't get electrocuted from the battery. However, it can be shorted and cause issues, so make sure to be careful with that. Don't allow anything that is metal or a conductor to cross between the battery terminals at the same time. Also, install the positive first and then the ground.
Next, turn the key off, turn all things off, and close the door. The noise you heard is because there was an immediate electrical draw on the battery from those components.
Now, as far as the aftermarket remote start, as long as it's properly installed, it should be okay. I personally am not a fan of them unless it is original equipment on the vehicle.
Here is a link you may find helpful. It explains how to change the battery.
https://www.2carpros.com/articles/how-to-replace-a-car-battery
Let me know if this helps or if you have other questions. Also, you won't get electrocuted from the battery, so don't worry about that.
If you have a chance, let me know if you get it together. Remember, turn everything electrical off and close the doors. That way, even if there is a spark or sound when you make the last connection, it will be minimal.
Let me know if I can help.
Take care,
Joe
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Thursday, July 22nd, 2021 AT 8:28 PM