I bought a new chain for 7 speed and added a few more links from the original one. I'm still confused because there is vibration on the smallest cog but the other ones seem to be fine.
I might consider just sending it to the LBS to solve the headache for me.
I did compare the two chains side by side and the old one showed significant wear, so it was a good call to replace it. The clanking sound is gone, but I still feel the vibrations on the smallest cog.
As requested, a few pics of my bike after a somewhat thorough clean.