It appears you have some ceiling drywall missing, your fire-stop. And some rafters/ceiling joists, and insulation. Use straps every 4' of unsupported pipe, the rest will depend on the application, Figs. 18,19, 21,22; http://www.fornobravo.com/PDF/duratech.pdf
With about 39" of pipe above the roof, some chimneys require that plate only on 18" and bigger pipe.... consult the fireplace manufacturer. Go on-line for their installation instructions.
I'll move you to HVAC for more responses..
Clothes taking longer to dry?
Clean the dryer screen in HOT water if using fabric softener sheets.
They leave a residue that impedes air-flow, costing you money.
Clean the ducting in the last six months? 17,000 dryer fires annually!