Macbook Pro is getting hot directly.

The battery has an cycle count of 980 and is almost going to his end. The magsafe adapter is new and almost 1 year old.

Cycle count is one important bit of information. According to Apple: "Your battery is designed to retain up to 80 percent of its original capacity at 1,000 complete charge cycles." ... so, in theory, even though your battery is near that count, what's more important is the battery condition. If you click on the battery icon in the menu bar, it should provide you with one of four conditions:

1. Normal
2. Replace Soon
3. Replace Now
4. Service Battery

Note: The condition value was also available at the same location in System Information where you found the cycle count.

When the battery is not charging the mbp is doing the same thing unfortunately. Or does this also has to do than with a old battery?

FWIW. I have a mid-2010 MBP that had the original battery and the condition was reported as: Service Battery. It couldn't run at all with just the battery alone and was always connected to power. In this state, it always ran "hot." Again, the location on the case where the battery is situated, became too hot to place on my lap. Once I replaced the battery with a new one, that heat issue went away.

Furthermore, as a safety precaution, I replaced the original MagSafe adapter with a new one from Apple. I would recommend that you only get these adapters either directly from Apple or from a trusted third-party source, like Other World Computing (aka, MacSales).

I would be suspect that a 7+ year old battery would still be "good" after all of these years; however, anything is possible. The reason I suspect the battery is that older or depleted batteries "heat up" when charging. Sometimes to where the notebook's case where the battery is located under gets almost too hot to place on your lap.

So, I think there is still two possibilities here:

1. The battery is past it's useful life, and/or Ref:

   Determine battery cycle count for Mac notebooks - Apple Support

2. The MagSafe adapter is faulty.

   Apple Portables: Troubleshooting MagSafe adapters- Apple Support

Something else you can do before replacing the battery is to run the Apple Hardware Test (AHT) to see if it uncovers anything amiss with your notebook's hardware that may be not related to the battery.

Use Apple Diagnostics or Apple Hardware Test - Apple Support

Is your 2011 MacBook Pro (MBP) still using the same battery? ... or has it been replaced recently? If the latter, is the replacement an Apple product or something you obtained from another vendor?

It will really depend on how you are taking these temperatures and if you are reporting them in Fº or Cº. If in Cº, then 95ºC is running too hot for the CPU.

With a temperature difference like that it sounds like the thermal paste has dried out and needs to be replaced. You'll need to remove the logic board to do that. If you're comfortable with electronics, it's something you can do yourself. I will link to a guide that shows you how to replace the heatsink and how to re-apply thermal paste.

For thermal paste I recommend using Noctua NT-H1 which has one of the best thermal pastes out there, and isn't electrically conductive. I use it for my gaming PC which is overclocked to the moon and back.

If you have re-applied the thermal paste and you still have a big temperature difference between the CPU and the heatsink, the chance is that the heat pipe has started to leak and therefore isn't transferring heat between the CPU and the heatsink as effectively, so you'll need to replace that. I will post a link to a video that shows you how heat pipes work. If you were to do it yourself, what you need to search for is "a1278 late 2011 heatsink".

MacBook Pro 13" Unibody Early 2011 Heat Sink Replacement - iFixit

How to Apply Thermal Paste - iFixit

What is a Vapor Chamber as Fast As Possible - YouTube

You CAN go to an Authorised Apple Service Provider, but there is a chance they wouldn't even look at it because it's considered a "vintage model". If you're not comfortable doing these jobs yourself, and Apple doesn't want to look at it, I'm sure you can find a computer workshop around that can do the job for you.