Do I need to protect the physical empty SFP port? What's a good way to do so?
Need to? Generally speaking no you don't need to do so. I have seen equipment used in construction trailers for years which have worked just fine when a SFP/GBIC is installed later.
However, I would recommend you do so. Why? Because there is the chance of causing a failure that could be more costly and/or time consuming than if you had put in a tiny amount of preventative work. Like many things, if you put a little more effort in when you have the opportunity, it will often save you (or someone else) a lot of time and/or frustration that could be avoided.
If you don't have something specific to the task, I personally like gaff/gaffer tape as it rips easily and tends to leave little to no residue when you remove it.
Do I need to protect the one/two ports in a SFP module? If so, how?
Again, need? No, but you should do so. If you don't have the caps to do so properly something as simple as a plastic bag or box that seals will avoid most of the potential problems. If something like that isn't handy, a small piece of the aforementioned gaffer tape will work in a pinch.
In any event, I always recommend getting and using a proper fiber cleaning kit whenever you make fiber connections. Always clean connectors and cables on both ends when making the connection. If you have it, some sort of fiber scope for inspections also helps.
I can't begin to count the times where a simple cleaning has stopped errors or low power issues on "problematic" fiber runs. Even with new equipment/cables that have never been used and have been capped, I often find that if you inspect them with a scope you will find traces of oil or residue from the factory present on the face of the fiber.
Let me say it again. Put in a little more effort when you have the opportunity and it will often save you (or others) time and/or frustration that can be avoided.
Should I remove the unused SFPs from the switch and store them elsewhere?
Let me ask, generally speaking, should you power off and/or unplug electronics you are not using? Same general answers apply.
First, electronics have a "life" expectancy. The longer they are in use, the more likely they will fail (excluding early failures often caused by defect). SFPs that are plugged in will be "in use" even if you connect no cable to them. While their MTBF (mean time between failure) may be significantly higher than the life of the equipment you are using them in, why tempt fate?
Second, it is a waste of power. While the power draw may be relatively tiny, it isn't to be overlooked. In data centers, there may be tight power/cooling budgets that any little bit helps. Or an organization may potentially have hundreds or thousands of SFPs that could be removed, multiplying that relatively tiny amount of power into something more significant (and costly). Finally, being green is good for everyone.