Do you need ”cel” here?
Apparently not. I left it out, and my answer was accepted.
In my opinion "cel" only makes sense if there are several mobiliere next to each other and only one is old
Why can't I write the verb after the subject? Does it change the maeaning?
Doua vaze frumoase sunt pe mobilierul cel vechi
No, it doesn't. You can also say: Pe mobilierul cel vechi sunt două vaze frumoase. As you can see, Romanian is more flexible than English. Baftă în continuare!
Why does "cel" come before vechi and not before frumoase?
"Cel" is masculine singular. "Două vaze" is feminine plural, so had to be "cele" if you want to use.
Why is the "cel" there at all?
why is it there? Does it change something in the feeling?
mobilierul cel vechi = mobilierul vechi
"Cel" puts a subtle emphasis and emotion on the adjective.