Question 1: Is it possible to take 100ml of medium with already fully developed bacterial culture inside and mix it with 900ml of pure medium to effectively grow another 1000ml of bacterial culture?
Yes, it will grow in theory if there's an energy source found within the medium.
This process would allow me to keep "cloning" the initial bacterial colony indefinitely without the need of purchasing freeze-dried samples every time I need to run experiments.
Yes, good strategy.
Question 2: Is it possible to keep the already fully developed bacterial culture in a 100ml medium for longer periods of time (months)?
The specific length of time that a culture will remain viable in a given storage condition is dependent upon the bacterial strain.
According to this article:
Being isolated and differentiated, Gluconobacter can be maintained on various liquid (beer) and solid media. Table 1 gives a survey on recommended solid media. Agar cultures should be kept at 4 °C and transferred monthly. Strains can be kept frozen at –75 °C in the presence of 24% (v/v) glycerol or dimethyl sulfoxide (10%, v/v). Freeze-dried strains will remain alive for several years.