If my old iPhone was reset to factory, will it reinstall apps I had on it previously?

If you restored from a backup after a factory reset, the apps will be reinstalled on your phone that you had on the backup. This may take some time if you had many apps.

To view if anyone else is associated with your Apple ID, go to Settings > [name on top], and scroll down to the bottom of the screen. Any devices listed there other than yours have used your Apple ID.

If my old phone was reset to factory, will it reinstall apps I had on it previously?

No, only the apps that were included with the iOS version will be reinstalled......unless you are planning to use a backup of the old phone that was made before the phone was reset to restore data to the phone again. Then....the other apps that you had on the phone will be reinstalled as well.

Can someone be hacked into my phone or account?

No one can hack your phone unless you have let them use your phone for a hour or so and also provided them with your Apple ID and Password.

Your iCloud account could be compromised if you have given someone your Apple ID and Password.

And my phone is getting really hot lately and that concerns me.

The phone is not overheating unless you see a message on the screen to that effect.