It is OK to go upside down as long as positive g is maintained throughout the manoevre, eg in a loop or barrel roll. For prolonged inverted flight where positive g cannot be maintained, special fuel and oil systems are required. My aircraft was solely for touring use and therefore without the special fuel/oil systems. It did however encounter lots of momentary negative g in turbulence and there were never any problems with battery or engine.
First off, here is the original battery tender. Although the name has become ubiquitous, like Kleenex, there is a reason they are called what they are called:
They (or similar items from competing manufacturers) are available in the battery maintenance section of every auto parts store in the USA, and probably Europe too.
Regardless of what kind of battery you get, you would be well-advised to install some sort of cutoff, either the key- or knob-type. I have found, quite by accident, that by disconnecting my batteries from the rest of the electrical system when the car is not in use, I have rendered my batteries absolutely immortal. The battery in my Cobra is 14 years old, and the Pantera battery is about the same age. There has been ZERO loss of performance from day one, because I religiously disconnect the battery after each drive.
You can get the kind with the green knob on E-bay for $5. The key-type switches aren't much more expensive; they are also available from Amazon, and just about every auto parts or racer supply retailer you can imagine. Auto parts stores probably carry them too.