First yes you can connect a laptop into a two prong outlet. Is it Safe? That's anybody's guess.
My easiest answer without out rewiring the apartment is to purchase a small UPS system for your laptop. KVA size depends on your computer equipment demands. It has no direct electrical connection to the supply side power. In other words it creates it's own power. This keeps you power supply clean and constant and it protects from surges and sages and requires no electrical knowledge.
If you would like to provide a little more protection. You could ground the source side power and bond the case (should be already done within the unit).
Good Luck
Get the freezer off GFCI. It should not be on a GFCI outlet; it's not that type of load. It has a metal frame with all the electrical bits in an impossible-to-access location, and you're not likely to drop it in the sink. Fit a single receptacle off-GFCI, and label it "Freezer only". Re-task that GFCI to a circuit where protection would be helpful.
There are at least 3 types of GFCI device: GFCI+receptacle combo devices (you know), GFCI+breaker combo devices (which look like breakers with a TEST button), and plain GFCI (which look like a GFCI+receptacle with sockets missing). All of them can protect a downline load. I'm glad you know that. Do not fit GFCI receptacles at locations already protected by GFCI. Do fit "GFCI Protected" stickers at those locations right before the inspector comes.
You're right, the downside to using receptacles/deadfronts to protect downline locations is it can be the devil to find the receptacle! Keep looking; it must be somewhere. It's also remotely possible that pulling a heavy load on the circuit has made a wire connection at a receptacle fail, typically a backstab connection. Those are very annoying to find.
15A receptacles are internally certified for 20A through-current, so 15A receptacles can be used on 20A circuits. A 20A GFCI receptacle might just be that. However, if the 20A GFCI has the "T" shaped neutral like the above pic, then it must not be used on a 15A circuit.
When an appliance trips a GFCI, that means the appliance has a ground fault. That's what GFCIs do. That's their one job. It's amazing how people are in denial about that. It's like if you taught them to detect steel with a magnet, and they try their toaster and it sticks, and they're all like "No way, this CAN'T be metal, there MUST be something wrong with my magnet!" And they try 3 more magnets and you're like dude...
That's how people are with GFCI trips.
You've performed due diligence; you tried it on other GFCIs. The answer is conclusive. The pool pump is a human-safety device (electrical drownings) so a ground fault is 110% unacceptable, and they also have a tendency for ground faults, so it's not a surprise. You can try a bench overhaul, but most likely into the trash it goes. For the freezer, it's faulting too and that's common, but no way. We're not throwing away freezers for that, because it's not a threat to anyone and a lot of brand new freezers trip GFCIs. Nature of the beast. Just make sure it's solidly grounded and call it a day. The inspector won't like it if it's a general-use receptacle; but he's unlikely to flag a dedicated freezer-only receptacle because he knows the score.
Best Answer
GFCIs (in proper operation) interrupt the flow of current when a ground fault is detected.
That is, if the amount of current flowing out of one of the sides of the socket does not exactly equal the amount of current flowing back in the other, it'll cut off power so that no electricity flows out of the outlet. (Some configurations protect "downstream" outlets as well.)
The possible safety benefit comes into play only when something is actually plugged in to a protected outlet, and the real safety benefit is realized when (a) something is plugged in AND (b) whatever that is has a ground fault that would otherwise put someone or some property in serious danger.
The other slight possible benefit of replacing the outlets before use is the possibility of discovering some existing dangerous wiring issue if it exists in the current outlets, but the odds of that are relatively low and the odds of you putting such an error in (especially if you do it yourselves!) seem a whole lot higher. If you're concerned about the existing wiring to outlets you aren't using, you can probably just turn off the circuit breaker to that circuit, so there won't be electricity in the outlets. This assumes you're not using anything else on the same circuit.
If you're not using those outlets, there's no benefit to replacing them right away, and there is of course a cost to doing so. You could buy replacements and wait on installation until some time when you have an electrician over to the house for something else, when the marginal cost of replacement is minimal. Then you can benefit from GFCI protection if/when you do start using those outlets, and (assuming they still work) have one less item on the next buyer's inspection report to help that buyer feel more at ease.