SDR stands for Software-defined Radio. A webSDR is a web site that has SDRs that people can listen to online via a web browser. This means you do not need any special equipment or hardware such as radios or antennas. You can listen to these radios also on mobile phones. There are also plenty of apps out there that connect to these web-based radios. Most webSDRs will have just about every radio frequency one can listen to including Shortwave (HAM), CB (Citizen's Band), AM, FM, Satellites, weather, military, and many more.
The information on this site assumes the listener is in the USA. I cannot speak for other countries. I also am not an attourney so I cannot give legal advice. However, it is known that it's always been legal to listen to these radio frequencies as long as you do not transmit on them without a valid license from the FCC and do not share the information you have heard or decoded. Anything that is public is legal to listen to. For complete information, please consult FCC's Interception and Divulgence of Radio Communications.
Some people do make recordings to keep a record of things. Laws vary from one jurisdiction to the next on what you can and cannot record. You would have to consult the laws in your area.
Unfortunately, not really. The reason is for the same reasons you wouldn't let those who are immature use the internet or watch certain TV shows or listen to certain podcasts. People can be very offensive in their speech in general and some that transmit on these frequencies are no exception. There are quite a lot of good, decent folks, but not everything on these frequencies would be suitable for everyone. While it is true that some kids do get into this hobby, I'd assume that they are well monitored by a responsible adult while using the radio.
Due to the nature of webSDRs and radio in general, there is no such thing as a
"safe" frequency. Most webSDRs have tabs at the top that give a hint
about what the contents of the frequency in that spot is. So you could also use
that as a guide in determining if that's a spot you wish to listen to.
The Freq section also has some interesting frequencies you could start with.
As with anything of that nature, the most ethical thing to do would be to contact the authorities to check into it. In this case, it would be a good idea to have a recording of the transmission (if it's legal to do so in your area), along with a log of the time, date, what was said, frequency, band (ie. USB, LSB, CW, etc.) decoded Morse Code (if necessary) and if possible, where the transmission would be coming from. This might be not so easy though without additional software. However, you could also provide the webSDR URL, and then look for the information of the radio you are listening to along with the radio's location. This does not provide where a transmission is coming from, however. It just gives you more information on the receiver. You can take note of the signal strength and that might give more clues as to how far away from that radio the transmission is coming from.
There are many reasons one would want to listen only. A HAM license is only
necessary if you plan to transmit on most shortwave frequencies (Citizen's Band
is one exception). You don't need a license to listen but you should still be
knowledgable of the laws as mentioned above.
Many people may not know for sure if they would want to invest in studying for a license, taking a test (which is required) and paying the fees for the test. They want to see what's out there first and see if it's something they would be interested in. Others may not want to (or due to health issues be able to) talk with others on the radio. Therefore getting a license would just be a waste of time and money to these people.
Others may not have the money for the license fee, the equipment or the room for the equipment (though you could transmit with a simple and cheap hand-held radio or even your phone using certain apps).
Still others might not be able to get to a testing site to take the license test, or may even be concerned about being profiled by the examiners and worried their scores might not be submitted. Generally in the USA this should not happen but some minorities and women may still be concerned due to the general public's view of their class in their local community, paricularly in other more restrictive parts of the world.
While having a license has advantages, if you just intend to listen to what is out there (and there can be some interesting things to listen to), then you don't need to spend time with a license. Alternatively, if you do want to just talk to folks on the radio but still not sure about taking time or getting a HAM license, you could try Citizens Band (CB) radio which (in the USA) does not require a license.