Yesterday I had a somewhat stressful flight out of a busy airport back to my local airfield. - After take-off the navigation "equipment" (a tablet) failed, the controller asked me for my position around a mile out, my response was incorrect as I was trying to troubleshoot the device, so he gave me a few Visual Reference Points to help out. - About 8 miles out, I saw a wall of fog & rain closing in from the left of my heading, it was coming in fast, went all the way to the ground and was certainly IFR (I was on VFR and am not instrument rated). I called the controller and asked about the weather, he said there had been unexpected reports of IFR conditions and not to succumb to get-there-itis. He suggested returning, which I declined for now. - Due to these distractions, I had stopped climbing, the controller called me to ask me to verify my altitude as there was high terrain around me, for which I was too low. - Shortly after this I encountered moderate turbulence. - The controller then called me to say we were going to lose two-way communication soon, he got weather for my arrival destination and asked me to switch to London frequency as he didn't want me not talking to anyone (I wasn't anywhere near London by the way). At this point, my brain became overwhelmed and I was unable to think clearly, I didn't change frequency, I did land safely but after landing realized I hadn't performed some of the pre-landing checklist items and had also gone the WRONG WAY around the circuit before landing (luckily no one was around). ***In these kinds of situations, should you telephone the departure tower to tell them you arrived safely, or is that just extra noise they don't need?***