Hi there!
Regarding the first, it could be a trace which is damaged, please check for any damage there. How are your battery springs, still OK? If there is corrosion on it, the same issue can occur.
Regarding the 2nd one, I advise to replace the left analog stick first and see how that goes. This requires soldering, but it's not very hard to do!
Here is the guide so that you can determine for yourself if you want to repair it or not: [guide|17887]
Please let us know how it goes!