Having some serious issues with my iPhone and need some advice

I'm going to these two issues which have been occuring with me for the past weeks-

 

1.) I am facing a problem with my iPhone 5's lightning port or the cable. This started happening all of a sudden; one second my phone is charging, and the other it is not. Even if it is slightly moved from its position, it would stop charging, and further shaking starts it again, so on and so forth. At first I thought the issue might be with my cable, so I asked my friend to bring his lightning cable to my house so we could test that. It happened again- one shake the phone will charge, another shake stops it. (Note that any kind of movement does this, not only shaking) I'm a bit skeptical about his (my friend's) cable too, though- it shows NOT CHARGING on his iPad while it is in fact actually charging. His cable is only 3-4 weeks old though, so this confuses me even more. I think the issue might be with my port, but as of now I cannot draw a valid conclusion to my problem.

 

2.) The second problem is that I've noticed my battery drains a **** lot faster now- ever since the first issue started. I manage to get my phone charging by placing it very carefully on the table and it charges overnight. However, when I pick it up in the morning, and read some news, it drains from 100% to 99% in ~60 seconds. This never happened before. Before this, it used to be at 100% for at least 10-15 minutes (might be even more). If I reboot my phone, it shows 100% again, but it still drains a lot faster now. I know because I've been using this phone for the past 4 months now, and I know when it drains and when it does nots

 

Please, help! I need some advice as to how I should approach this problem. My phone is in the warranty period, however, I would like to have an expert's opinion first.

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