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Actually most of the content of cat poop is similar to that of other animals — cows, birds, etc. that we pay others to collect. I am not promoting cat feces as a fertilizer, but it isn't the end of the world either. The balances of nitrogen, potassium and potash aren't quite the same, digging up cat feces is not a pleasant gardening experience and there is the slim risk of infection.
Cat feces also contain parasites for roundworm, hookworm and tapeworm. However, if gardeners wear gloves, wash their hands and rinse and wash any harvested crops, they will greatly decrease any chance of infection.

Yes it needs drainage. The best of course is if you can pull everything out and start over with holes in the bottom, no tarp and raise the box a little with some wood or bricks underneath.
But the shortcut would be to drill some holes along the lower edge of the wooden box, where the bottom of the soil level is? Although if the tarp comes up on the sides, inside the box you would have to drill the holes clear through the tarp also, and that could be a complication.
Another option is to not water anymore than you have to. Just moisten enough to keep the plants alive but not so much as to waterlog the soil.

Sure, during heavy rain periods or storms you can cover your plants. Be sure to uncover as soon as the rain stops!

Looks fine. The key is to provide adequate water and fertilizer to support all.
https://www.domyown.com/dr-earth-total-advantage-rose-floral-fertilizer-p-9491.html

Yes, fall clean up of plant debris is very important. The next step is to nourish the soil and improve soil tilth by putting several inches of tree leaves over the soil. Some advise chopping or running over leaves with a mower; most leaves don't need this but maple leaves are well-known to mat together creating an anaerobic environment that inhibits breakdown. Another concern is that many a butterfly chrysalis and other beneficial insects spend the winter rolled up in leaves or as eggs attached to leaves; mulching or chopping destroys these creatures. One solution to matting of maple leaves is to mix the leaves with compost. 4 inches sounds about right. So get out there and take your neighbors' leaves when they are put out for compost pick-up. Fall is also a good time to work in nutrients for correcting deficiencies and pH problems. These amendments need time to work so fall is a great time. Withhold nitrogen; it passes quickly through soil and will be gone by springtime.

It isn't necessary and is actually not a good idea to till the soil in your raised bed. It turns out that tilling does more harm than good. I would chop leaves with your mower and put several inches over the beds. If leaves aren't available, put down a couple inches of compost. Otherwise winter prep is making sure you remove all plant material so any unwanted germs or bugs don't overwinter in the bed. https://www.gardeningknowhow.com/edible/vegetables/vgen/veggie-garden-winter-prep.htm