Macbook feels a lot hotter than usual; are these temperatures normal? I have an early 2015 13" Macbook pro with a 3.1 GHz Intel Core i7 processor.

I've been having some battery issues lately, that could be been attributed to charging my laptop and plugging in foreign USBs (I bought this iPhone 7 charging cable in Italy that doesn't seem to fit my macbook USB port very well, and it doesn't seem to allow my macbook to recognize the device, although it does allow it to charge) into my macbook pro when I was overseas back in July, or it could just be my battery is deteriorating (I have a 850 cycle count). 

The first time I noticed issues was back in mid July when I was in Italy. Macbook battery bar showing as red; battery % jumps around; battery condition normal; out of US charging
But those issues were quickly resolved when I reset the SMC.

Last week, I started getting a "Service Battery" warning on my macbook. I've tried resetting my SMC a few times, but the error remains, so it appears that my battery will soon reach its life expectancy. 

Today, I noticed that my macbook feels much hotter than usual. I'm not doing anything computationally expensive, so I have no idea why it's getting hot, and I'm wondering if it's connected to the battery issues I've experienced recently. I also checked activity monitor, and nothing appears abnormal. Below is the output from Macs Fan Control.

Are the temperatures way too high? I don't know why its reporting 45C for the ambient temperature. It's about 86F (33C) in my house.
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.