NMS8250 battery(?)

Yes, they have different charge characteristics, but this only comes into play when you want to fast charge the batteries.
This doesn't matter when it is used like in the NMS8250 since the charging current will be around 2 - 12 mA and no measurement of voltage or temperature is done.

Another reason you might not want to use NiMH for the RTC battery is that it has a higher discharge rate, but if you use your MSX every now and then it shouldn't be a problem.

Because this item is no longer available, an update! The new article code is:BANM390SC1. It's the same as the NIMH-90-1. You can find this @Nedis, or search for this component with the above article code.

On Dutch webshops:

https://www.todotipo.nl/elektra-voeding/batterijen/telefoon-...

https://www.bol.com/nl/nl/s/?searchtext=5412810319466

https://nedis.nl/nl-nl/product/elektra-voeding/batterijen/te...

No, because these are solder lips, and the original has wires. What you can do is cut the original near the battery (not on the pcb side, but closer to the battery), and solder the old wires to the lips. You can shorten the solder lips on the battery if you want. The benefit is that you don't have to take the whole main-board out. There is no difference, because somehow you must solder wires on the battery to fit in the main-board.

The only thing to pay attention is to solder it quick and good, not too long because this is bad for the new battery then. So proper & quickly solder on it will do the job. But not too quick, because then you will get a cold solder joint. Of course you can look further to a version with wires like Hans have he mentioned in one of his last messages.