While not legal advice:

In general, you can copy and create your own works for personal use as long as you keep them to yourself. Copyright is usually enforced on distribution, so if you don't distribute, nobody cares.

Free licenses (MIT, GPL variants, Apache, BSD, and so on) allow you to copy and create your own works and distribute the work freely. Free licenses allow you to distribute your work if you share the source code, and some (MIT, Apache, etc) allow you to distribute the work even without sharing your source code as long as you provide the source code for whatever was licensed (like a library you're using that's MIT licensed).

The licenses all have different restrictions, so it's good to research a license before you use something licensed that way. For example, AGPL, GPL, and LGPL are all different, and some licenses may require you to rename and rebrand something if you create a fork of it.

Typically yes, a free / open-source software license gives the user the right to use the program, to spread it around, and to create derivative programs based on the original source code, as long as the new derivative program follows certain rules.

For permissive licenses (such as the MIT license), the rule is something like "put this acknowledgment somewhere the user can see", if you've ever seen an "Open-Source Licenses" menu item somewhere, that's where they usually put these.

For "copyleft" licenses (such as the GPL), the rule also requires that your modified version is also distributed as open-source under the same conditions.

Most definitions of free or open-source licenses also require the license to impose no additional restrictions on how, or for which purposes, the software can be modified. The RAR archive extractor, for instance, is not open-source, because the license for its source code prohibits it from being used to make a program capable of making RAR archives. Some developers add conditions to restrict undesired uses, such as commercial or military use of their software. These licenses are likewise not considered "open source", but rather "source-available".