This is a common question.
If your organization has its own server space, the answer is most likely to put your videos on your organization's server. This is especially true if your organization doesn't charge you or have strict or weird rules. Many years ago, when I worked for The University of Iowa, they had a “video server,” and that's where I stored my videos. However, when I worked at St. Ambrose University, some administrators believed that anything put on one of their servers became owned by the University, so your hard work developing great videos could be given to any instructor. (This is why I chose to buy my own server space. Many universities recognize that things created by instructors are theirs, but not all schools.)
When I worked at St. Ambrose University (SAU), SAU did not have a video server. So, St. Ambrose would always prescribe using YouTube. It cost SAU nothing. However, one drawback of YouTube is that any video you put there is licensed to YouTube. This means that YouTube can do anything with your video. This also means that any other school or instructor can use your video in their courses for free! Yep, you do all the work creating great videos, and everyone else can use them. At SAU, the IT staff didn't care that you put in the effort to create great videos; they cared about their budget (or lack thereof).
You might find some free servers, like Techsmith, but typically, you are limited by some storage space rules.
One of the most popular "paid-for" video hosting platforms is Vimeo, which I have been using since 2020. Vimeo respects your video licensing rights.
Sometimes, your LMS is hosted within your organization, which is similar to "On Your Organization's Server." However, sometimes, your LMS is hosted elsewhere.
Be careful! If you upload your videos into your LMS, it can grow and cause backup problems, especially when larger backups require more server space.
In my situation, I pay for my LMS server, and it has limited storage space. If I were to store videos in my LMS, I would need a lot more server storage, making it a less cost-effective solution for me.
This includes products line OneDrive, GoogleDoc, and iCloud. Common issues with these solutions include the requirement for a login, the lack of a direct URL, and the necessity to consider licensing rules.
This is a common question, and the answer is "you can't." Most people own smartphones that can be pointed at a computer screen, put into camera/video mode, and record anything. It seems a bit crude, but it happens, and there is no way to prevent this unless you can take away their smartphone.
People have other options to download videos. For example, sometimes you can add plugins to your browser that provide video downloading. Sometimes you can purchase applications that download videos. And there are "screen recorder" applications that can "record" anything shown on a screen. I like using Camtasia for this purpose.
The best one can do is to make it difficult for people to download your videos, but you cannot prevent it. This is not only true for videos, it is true for anything that is displayed on a computer screen.
In my courses, I prefer to let students download my videos. I aim to make it easy for students to learn from my videos. And if it is easy, students may spend time in my courses instead of in their other courses.