Do you need ”cel” here?
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.