Macbook Pro 13" (Mid 2014) SMC problems?

My 13 inch Macbook Pro has been having various issues:

• My fan doesn't speed up when temps go up. I've installed "Macs Fan Control" to control the speed manually, but this isn't ideal.
• Sometimes it randomly crashes. I have no idea why. At first I thought it shut off to prevent damage by high temperatures, but it also happened when it wasn't under heavy load.
• It often doesn't detect my Magsafe being plugged in and it doesn't charge. Even after unplugging it and plugging it back in, it won't charge.

I have tried resetting the SMC and PRAM numerous times, without any improvements. I also haven't spilled any water on my computer. I think these problems started occuring when I installed iStat Pro to monitor temperatures, but I've uninstalled it since, hoping this would resolve the problem. It didn't.

What could be causing these problems and how would I fix it?

Thanks in advance,

Tijn

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