I'm not sure why you actually need a smartphone for just calls and texts but the one you've got (which is a little long in the tooth, as it's been on the market for 7 years) only supports a 3G connection. That's not important though for just calls and texts. (4G or 5G offers much faster loading of web pages but makes no difference to calls and texts).
The letter 'H' tells you the type of signal available to your phone. You might also see 'E', '3G' or 'H+' displayed there at times, depending upon what the local mast can provide:
https://support.freedompop.com/app/featured/answer/id/3238
The pinging might well be related to incoming emails but your phone won't be getting any unless you've actually entered details of your email account into it. So have you done that? (If so, you appear to have been wasting your time!). To stop it pinging though (for whatever reason) you need to go into 'Notifications'. That's probably achieved by going to 'Settings', them to 'Sound & Notification'. Then (if the pinging is being generated by a particular app, such as the email one), you'll need to go into 'App notifications' and tap on the relevant app (which is presumably the email one) to get to a point where you can disable all notifications from it.
I'm a bit lost with the other things you've mentioned though!