You've asked questions here that cover an awful lot of ground so rather than try and answer it myself I've entered your questions on ChatGPT which has made a pretty good job of answering. See the attached PDF which I think answers your questions very well. Anything more specific come back here and ask again.
You don't need to obsess too much about the exact antenna length for receiving until you get to critical listening, i.e. extracting every last drop of signal. For example, if you want to receive long distance signals on VHF/UHF, then you are talking about a multi-element antenna cut specifically for a band (say the 2m amateur band) which is directional with high gain and is steerable, such as a Yagi etc.
For general "just see what's about" type listening you will get by just with the telescopic antenna for now and if you want to try optimising it, use the rule in the PDF I've attached which gives a quick rough formula for tuning/adjusting the antenna length to approximately 1/4 wavelength which is the ideal for a small whip antenna.
If you are looking at receiving much lower frequencies than VHF/UHF with an RTL-SDR, shortwave broadcast bands for example, then you will need to start looking at antennas optimised for LF/MF/HF (which broadly speaking covers a range of 500kHz to 30MHz) then you need to look at putting up a length of wire several meters long or, possibly a better bet for a "one antenna covers all" (receive purposes only), a broad-range loop antenna like this:
https://midsussexars.org.uk/feature-art ... -amplifier
The big issue these days with antennas is trying to place the receiving element away from noise sources. Just trying to use a telescopic whip indoors right next door to local noisy power supplies etc that are to be found in most home, will likely lead to disappointment as a lot of the time you will struggle to extract a signal that exceeds the local noise level. Nevertheless, those noise source tend on the whole to produce noise at the LF/MF/HF frequencies (up to 30MHz) and above this you stand more chance with the whip of receiving some local signals, like ham radio repeaters on 2m/70cm for example, or VHF FM broadcast radio signals
Max