Q: Since a few days my w-lan connection is extremely slow, while the Router seems to work perfectly. At the same time I seem not to be able to update with time machine on my Time Capsule

When connected to the network, press and hold the Option key and click on the wifi icon in the menu bar and post a screenshot of the window that opens

I asked you to post a screenshot of the window that opens when you press and hold the Option key and click on the wifi icon in the menu bar, not to run diagnostics.

The window looks like this

No, that is not it, please follow Illass's instructions

That screenshot shows you are connected to your iPhone's wifi hotspot, not your wifi network. Thus, you can't connect to your Time Capsule and the phone's connection to the internet is slow

I need that screenshot when connected to your network.

Connect to your network and take the screenshot and then connect to your phone to post the screenshot

Nothing looks amiss. You are connected to a 5GHz network with a good Tx Rate.

Try creating a new network location

Using network locations (Mac OS X v10.6 and later) - Apple Support

You also said "I seem not to be able to update with time machine on my Time Capsule".

Do you mean that TM can't see your Time Capsule?

When you are having problem. look At the window  again and look at Tx Rate and makes sure you are still connected to the 5GHz window

on your connection to LS26870-LAS_5GHz:

you are using 802.11n mode on channel 161 in the 5GHz band. Your 40MHz signal will spread up and down the spectrum, and parts will be interfered with by other Routers using nearby channels.

Your signal strength of -67 less the noise level of -86 gives signal-to-noise of only -19, which is fair to good.

Your transmit rate of 243 is twice the baseband speed of 121.5, which is next-to-the fastest baseband speed possible (135 is the fastest). You are sending your signal using two antennas, and your actual signal is the difference between the two antennas' signals.

That is not the fastest possible, but you should not be having connection issues. There are a few things you can check:

Be sure IPv6 is set to link-local only.

Be sure you have turned OFF "wake for network access" in energy saver unless you intend to actually use it.

Create a new Network Location as lllaass suggested.