Humming and Vibrating

So i have my 2010 Tacoma TRD Sports edition. On Thursday, my wife was driving the truck to work and it shut down on her. I gave it a jump start while I arrived and drove it back home. Since then it has made a humming sound as soon as it turns on. I thought it could be the alternator, so i disconnected the battery while the engine was on and it stayed on. I took off the V-belt and it was in good condition. Now as i drive and brake at a stoplight or atop-sign the RPMs drop to a little less than 500 and the truck starts vibrating. Hopefully it’s something like the spark plugs since I haven’t changed them since I had the truck in 2013.

 

plugs
Throttle Body and MAF Sensor could probably stand a cleaning as well

 

Negleted trucks dont last long,never changed your plugs in 8 years,no wonder you are having problems.

 

maybe he only drives 5k a year

 

First of all never disconnect the battery with the vehicle running, it can cause voltage spikes which can damage the alternator as well as the electronics of the vehicle.
The charging system should be checked with a multi-meter set to volts DC, with all loads on (blower on high, headlights on, etc) battery voltage should be 13-14.5 volts.
The low idle is probably a dirty throttle body, clean the throttle body (and Mass Airflow Sensor while your there) reassemble and let the truck idle for a few min so it can relearn it's base idle and you should fix your problem.
Plugs are a 30k Mile item on the V6 engine and 100k Mile item on the I4 engine.