Berlin is a particularly difficult city for a one-day visit if you happen to like both political-history and art sights. I hope you are lukewarm about at least one of those! You're smart to figure things out ahead of time. Get a map and mark locations of things you want to see so you can figure out what is geographically possible.
Some random thoughts since your target list is quite different from my 2015 list, though I visited the Topography of Terror (10 AM - 8 PM at this time of year) and found it very interesting. From experience I can tell you that they do shoo visitors away from even the outdoor part of the display just before closing time.
I've mentioned some other possibilities below just because they might give you something to do early or late. There's no end of interesting places to see in Berlin.
The Museuminseln museums are huge; you can spend 3-5 hours in each one and not see everything. They often have hour-long lines during peak vacation season. (I don't know what happens at other times.) I'd be tempted to skip that on a one-day trip. At most, you might be able to see one section of the museum that interest you most. (I'd suggest the Pergamon Museum unless you are a big painting fan.) I think you'll find that the museums open at 10 AM, but I haven't checked.
You can Google the name of the attraction and easily find its official web site, where the opening hours will be given (usually under "Visit"; perhaps under "Contact Us"). Be careful about seasonal hours. Visiting hours may be cut back at the end of September. And be aware that some places stop selling tickets/allowing entry 30 or 45 minutes before closing time. This is normally mentioned on the website.
Without exception, every government-run museum I visited in Berlin required me to check my standard-size purse. So I would assume that any object you are carrying must be checked. There will be lockers and/or a staffed counter. In my experience there's no charge at the counter but the lockers require 1-euro or 2-euro coins. No change is given for 2-euro coins, so be sure have several 1-euros.
Your best bet for something that opens before 10 AM or stays open late is probably a non-government-run sight, i.e., a commercial, money-making one. The House at Checkpoint Charlie is a small (tourist-mobbed at times) museum-like space that I found extremely interesting. It's open daily 9 AM to 10 PM at this time of year. The equally crowded DDR Museum (life in the DDR) is open 10 AM till 8 PM except on Saturdays, which are 10-10.
I'll bet someone does evening walking tours. There are at least two companies offering "free" introductory walking tours (tip the guide, they must pay the owner for each person who shows up), plus regular companies. A variety of walking tours is available, but I don't know what goes on at night. I'd prefer to do that rather than take a hop-on/hop-off tour, but plenty of folks like HOHOs. Just be sure you know how frequently the buses run. I've seen long lines of people waiting for them in some cities, and that's the last way you want to spend your time on a one-day visit. Berlin's sights are very spread out, and unless you're very lucky in the location of your chosen destinations, the S-Bahn/U-Bahn will be a faster way to move around.
There are boat rides on the river; not sure about their schedule but there's probably something at night.
The Berlin Wall Memorial on Bernauerstrasse has a major outdoor component. The Open Air Exhibition and Memorial Grounds are open 8 AM - 10 PM. The Documentation Center has more limited hours, 10 AM to 6 PM.
The outdoor (memorial) part of the Memorial to the Murdered Jews of Europe is open 24 hours a day. The visitor center is 10-8 through September, then 10-7.