Macbook feels a lot hotter than usual; are these temperatures normal?
Those temps seem fine to me. 

MBP models usually range from about 40ºC (104ºF) to 100ºC (212ºF) depending on whether the CPU is idle or under load. CPU temps (just like ambient temperatures) typically have a bearing on GPU temps too, especially within the extremely confined spaces of a MacBook. 

If you'd like, you can refer to the Intel Mac Temperature Database to see the various temperature ranges reported by users. You can also filter the list by model etc.

As for your battery, it's also clear that it needs replacing. MacBook Pro batteries have a life expectancy at or around 1000 cycles.  It's not uncommon for batteries to exceed or fall short of this number; as every user is different in terms of what they use their computers for and how/when they're using AC power etc. So the 1000 cycles is just an estimation of how long it can last. 

Since your battery needs replacing, it's not contributing as much to the overall power source mix for your MacBook Pro, so this could explain an increase in temperatures - although the increase could also be explained by other factors.

As an aside, the cable you bought in Italy is most likely a charge only cable (i.e. many of the cables sold at fuel stations etc only support charging and not data transfer), so that explains why this cable will charge your iPhone but not allow data transfer. Regardless, it's unlikely to affect the temperature of your MacBook Pro.