I have a center handle flue (stuck open) with an opening of 5"x30". Will this 8"x32" fit?

That size Flueblocker is right for the flue hole size of 8x32. If you can remove the damper handle by pulling the cotter pin where the handle meets the damper door, then remove the handle before you install the Flueblocker. However, If the handle is welded or bolted onto the damper door, you will need to cut the Flueblocker to accommodate the handle sticking through.

Do you make this in 7”x36”?

We do have a standard 13x35 (actual size is 14"x36") or a 9x45 (actual dims are 9.5x46). Either of which can be trimmed to fit a 7x36 hole. Although, I would recommend you go with the 9x45. Or we can make a custom size to your exact specification.

Can plastic be put on top of it when installing to avoid it getting damp?

You can do that if you would like....but the product is WOOL. Because it is WOOL it did not suggest plastic over it...your choice. I will add something here.. if you need to cut the product....try to leave as much of the pad on as possible..open the seams and trim sparingly. I ordered a VERY large one I tacked a piece of flexible plastic across the top part that goes into the chimney to give it more firmness as well as it to catch the inside of the chimney for support. It is doing its job.

Do i have take out the old damper, Too use this flueblocker?

This 8x24 is for a small wood burning fireplace. If you do have a damper and you want to install this below the damper, you can. But you may have to either remove the damper handle or cut a slit in the wool pad to accomodate the damper handle. Some people choose to open or remove the damper door and use the Flueblocker in lieu of the damper door since it offers a tighter seal. There are quite a few examples, photos. A d diagrams on the Cleverly Solved selector tool site.