Učim se besedišče za mobilne telefone<em> (you use accusative here. It's a pretty unusual sentence, though. "Učim se nove besede, povezane z mobilnimi telefoni" is more likely to be used)</em>

Danes ne delam in se učim besedišče za mobilne telefone. Kaj pa ti meníš?

phone number: telefonska številka
cell phone : mobilni telefon (ali prenosni telefon??) <em>(mobilni telefon is correct. "Prenosni telefon" is for wireless home phones. If you're using the word informally, you can also use "mobitel" for a cell phone.)</em>
cell phone number: mobilna telefonska številka
smartphone: pametni telefon

parts of a cell phone : deli za mobilni telefon 
screen : zaslon
keyboard : tipkovnica<em> (you always use nominative if the word is not used in a sentence)</em>
case : ovitek
phone charger : polnilnik
battery : baterija
camera : telefon s fotoaparatom
speaker : zvočnik
wifi : Wi-fi
SIM card : SIM kartica (???) <em>(correct)</em>
button: gumb
on/off button: gumb za vklop/izklop

Settings: nastavitve (za iPhone, na primer)
sound : zvok
airplane mode : način v letalu <em>(in menu it can be translated this way, because all of us know what it should mean, but this phrase by itself doesn't make much sense.  If you add a colon it looks better and makes more sense. "Način: v letalu")</em>
silent : tih
silent mode: tihi način
vibrate : vibriranje <em>("vibriranje" is gerund of "vibrirati")</em>
mute: utišanje <em>("utišanje" is gerund of "utišati")</em>
volume : glasnost  <em>(nominative)</em>
ringtone : način zvonjenja (??) <em>(you could also say "melodija zvonjenja")</em>
signal : signal
connection : telefonska zveza
Put your phone on silent : Dal telefon na tiho <em>(it depends what exactly are you talking about. If you're saying to someone else to mute the phone, then you say: "Daj telefon na tiho." If you're using neutral sentence then you say: "Dati telefon na tiho")</em>

experiences
voicemail : tajnica? glasovna pošta? <em>(both is correct, "tajnica" is for informal and "glasovna pošta" for formal use)</em>
to leave a voicemail : pustiti glasovno sporočilo/pošto  <em>("pustiti sporočilo" is for informal use. You can leave out "glasovno")</em>
a call : poziv ? klic ? <em>(both is correct, "klic is more likely to hear and safer to use as "poziv" can mean several different things)</em>
missed calls : neodgovorjeni klici
wrong number : napačna številka 
emoji : emoji <em>(I'm not sure if any of words for it already made it in the official dictionary, but you can say "smajli", "emotikon", "smeško")</em>
phone upgrade posodobitev telefona
app : aplikacija
to download: nalagati
to download an app : nalagati aplikacijo
to turn on : odpreti prižgati
to turn off : zapreti ugasniti
a text : SMS
to text : poslati kaj po SMS-u -- admittedly I haven't figured out the function of "kaj po" is <em>(you can use "poslati SMS" if it's easier for you. It's also more accurate direct translation. "Poslati kaj po SMS-u" sounds strange because here you have "kaj" as substitute for an unknown object. If you'd know the object, then you could say "Poslati informacijo po SMS-u")</em>
toll free number : brezplačna [telefonska] številka
low battery : zmanjkovati baterije
selfie : selfi

phrases : rekla <em>(You have written it in plural in English so I also corrected it in plural :) you can also say "fraze" or "fraza" for singular)</em>
You called the wrong number : Poklicali ste napačno številko.

Sources: lots of googlingkkkkkkk
to check out later: http://citymagazine.si/clanek/5-najboljsih-mobilnih-emoji-aplikacij-ta-hip-app/