My phone is deleting apps and acting very slow. How do I fix it?

[AC Question]

I got an Android Moto G for Christmas. I didn't set it up, my parents did. In about March it started acting really slow and this app popped up every time i turned it on called App Widget. But, the app never opens. However, I didn't download that app, I don't know where it came from. About 5 days ago I purchased an SD card for space because this phone didn't have a ton of space. The first day it was fine, it was about as fast as it was when i received it. However, the day after i got this card, i tried to update an app and it uninstalled it. I thought ' Maybe I clicked the wrong button'. I tried again to install it but it wouldn't let me. I tried a third time and it worked. 2 days ago, i went on my phone again, 3 of the 6 apps I put on it were uninstalled. But they showed up under my apps. I reinstalled all 3 again and they all updated on their own. Yesterday, I went back on my phone and the same thing happened. The 3 apps were gone from my screen but listed under the apps in Settings, but when I went to google play, they were uninstalled. I would like to know how to fix this. And no, they were not trial apps, I've had them on the phone since I got it.

 

[belodion]

Does the problem persist in Safe Mode?