Check the range of the mobile network, see this Apple article: If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
Check also the Wi-Fi network, see the following Apple articles:
Connect to Wi-Fi on your iPhone, iPad, or iPod touch
Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network
If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support
Changing Apple ID password,
Then see this Apple article: What to do after you change your Apple ID or password
What to do after you change your Apple ID or password - Apple Support
See also the following Apple articles:
If you can’t download or update apps on your iPhone or iPad
If you can’t download or update apps on your iPhone or iPad – Apple Support (UK)
Require a password for App Store and iTunes purchases
Require a password for App Store and iTunes purchases - Apple Support