I noticed that the rechargeable batteries are slightly thicker than the normal batteries. However, by "slightly" we are talking about fractions of a millimetre. In the case of a template cast to the hundredth, this can be a problem because the bodies do not fit into the shell. I have been using the batteries in various devices for years: Telephone receiver, clockwork, computer mouse, remote controls of HiFi components etc., with me the deviation has never led to complications. But I can understand why there might be a problem with the accuracy of fit in your area of application. I don't see a solution, except that you switch to normal batteries.
I don't think that Power or Endless make much difference here.
There are more important factors.
I use batteries with a large capacity whenever possible and operate almost all devices that actually need batteries with them.
It should be noted that rechargeable batteries only deliver a voltage of approx. 1.2 volts, whereas batteries deliver 1.5 volts.
This means that a rechargeable battery has to supply more current to generate the same power and therefore often lasts much less time than "real" batteries.
In addition, wireless phones often have charging stations, but these are not very intelligent - which means that the battery suffers in the long run.
But these things are the same for all batteries.
The Endless is completely sufficient for a wireless telephone in the home. The capacity depends on the duration of the call. For normal private use, the 750mAh is sufficient for several days of stand-by operation.
These batteries are nickel-metal hydride (NiMH) type and can be recharged using a compatible NiMH battery charger designed for C-size rechargeable batteries. The charger must provide the correct voltage (1.2 V per cell) and be suitable for NiMH chemistry. Charging typically involves placing the batteries in the charger with correct polarity and connecting the charger to a power source until charging is complete.
Note that the Varta plug chargers mentioned in the sources are designed primarily for AA and AAA NiMH batteries, so you will need a charger that supports C-size NiMH batteries specifically. Always follow the charger manufacturer's instructions for safe and effective recharging. The charging time depends on the charger's specifications and the battery's degree of discharge but usually ranges from a few hours to overnight.
No, a charger will not be included. The "Rechargeable battery + charger" is marked with product type. This means that this product is filed in the category "Rechargeable battery + charger". This has nothing to do with the scope of delivery.
The batteries usually have a size indication, such as AA or AAA. If you are not sure, you can also measure the battery and indicate the diameter and length. The manual, inside the remote control slot or cover, or on the battery itself should normally indicate the designation.