1.) Does this permission notice refer to this sentence, or to the paragraph starting with Permission is hereby granted...?
The phrase "the above copyright notice and this permission notice" refers to the "Copyright" line(s), the paragraph "Permission is granted..." as well as the paragraph "The above copyright notice shall...".
As for final paragraph in the license, the capitalized text "THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY ...." My opinion is that the requirement to reproduce the copyright notice and permission notice does not explicitly include this paragraph.
That is, you could probably omit the warranty disclaimer paragraph if you wish, without violating the MIT license itself. However, if you choose to omit this paragraph, you will be the one who takes any consequences for that omission. For example, if you're selling the software as part of a product and you have a legal reason not to disclaim the warranty, then you as the seller will then have the implied liability in that situation. Please check with a lawyer for the specifics if this situation applies to you.
2.) What does use mean? Is it a very broad term and refers to any instance of me either importing, including, linking, ...any part of the Software?
Yes, "use" in this instance means you may use the software generally in any way that would normally require permission under copyright law. If you read the whole phrase, the answer to the rest of your question will probably become clear:
"... including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, ..."
The phrase "including without limitation" makes it clear to the reader that the following list is not exhaustive. That is, you are definitely allowed to "use", to "copy", to "modify", to "merge", and so on, the Software. But the phrase "including without limitation" makes it clear that other things not specifically on that list may be included as well as permissible.
Computer programming concepts like importing, including, linking, and so on, tend to involve a combination of copying, modification (e.g. compilation to bytecode or link-time optimisation), and merging (since linking a piece of software to another effectively merges them). Since the MIT license specifically gives you permission to use, to copy, to modify, and to merge, then I believe it's safe to say that all of the computer programming techniques mentioned above (as well as others techniques that go by different names but which perform similar actions) are permitted as well.
3.) Where exactly shall the copyright notice be included?
The license text only requires that it "shall be included" without saying exactly where or how. To answer this question reasonably, I think we need to consider the details of how you are distributing the software.
For example, if you are shipping the software in a traditional way, in a box with CDs, DVDs, documentation, etc., then one way to include the MIT license text is to print it out and include it in the documentation.
Maybe the above situation sounds a bit old-fashioned today, but in fact it is still in current use in particular for automobile manufacturers, most of which include MIT licensed software somewhere in the automobile computer programming. A common practice for this industry is to include a small CD or DVD or some kind of medium along with the automobile user's manual, which reproduces the license text as required, along with any source code (if that is required for some of the open source software).
For digital-only distribution (e.g. to download from an App store), there are various ways. A popular way in this situation is to include a menu item somewhere in the App (usually with a name such as About, or License Information) which shows all of the required information and reproduces any license notices as required within the application itself.
4.) What does to deal in mean?
Deal in means to supply something, usually for the purpose of a business. By using this phrase ("to deal in the Software"), I believe the authors were trying to make it clear that you are allowed to do all of the things for the purposes of a business as well.
- [What if I don't distribute the software itself, ] ... but rather give a pom.xml or a requirements.txt and leave everything else to the user, am I liable in any way under any license? ...
Here is one way of interpreting mechanisms such as pom.xml or requirements.txt: by mentioning package identifiers, URLs, etc. in these files, even though you are not distributing the software itself, you are still distributing computer instructions that cause that software to be downloaded, more or less automatically. Therefore, you should still make reasonable assurances that this process happens in a license-compliant way.
For software licensed under MIT, for example, you should try to ensure that any kind of instructions in your dependency file(s) also cause the package environment to download the MIT license text as well as required by that license.