No way your STBX should have access to your account. If his name is not on the account then he needs to be shut out.
I hope the furniture lifts your spirits up. Sometimes resolving material needs like that can help one's PMA. I was sleeping on a lousy air mattress for months right after the separation began. When xW later found out I bought a new bed and some furniture to go with it (nothing that expensive, mind you) she obviously had a cow. She later threw that in my face -- she was obviously perturbed by it. I think she must have relished the thought of me living in spartan squalor indefinitely but then I had to go and ruin that for her.