These questions together are big. I can't say much to your reformation-question but I can answer your other questions. (I try to answer it in context and hope i don't run to far away^^)

How did borders work within the Holy Roman Empire? : The term „borders“ with its modern implications is not very practical for the medieval Holy Roman Empire. That is, because today borders imply a closed and fixed area of land, that is at least to some degree independent from the surrounding areas (no matter if a country like Germany in Europe or a federal state in a Republic like Bavaria). This idea is not suitable for the HRE in the middle ages. While there is a development over the centuries within the HRE, that ultimately leads to such more or less strictly and clearly separated areas, this wasn't the case for the large part of its history. Instead of closed areas the noblemen or clerus controlled several rights that could concentrate in one area so much, that it was under „full“ control. For example: Let's say you, /u/zombathon , are a count in the HRE. You have a big bundle of rights that resemble your status. You can have control over forests, over fishing, over „law/court“ or even protective control over a small church or abbey. Now you might have all those rights in the town A and its close related land, but in town B you still could just have the control over the forest. The fishing rights belong to someone else and the the control over law belongs to a third person, to give you a impression of how complicated it can get.

 

What were they like in the final years of the Empire compared to the start? Over time some powerful (and lucky) dynasties could concentrate the full rights over not one or some, but many smaller areas, leading to a big area under their control. The further this proceded the closer you get to borders in a modern sense. The Development can be described as a process of concentration of rights leading to a concentration of closed land-complexes.

 

How where they affected by inner HRE wars? The common reason for conflict within the HRE is based on exactly that model of „property“ and status. When two or more people have rights at the same place, it shows already the possibility for disagreements and conflicts. This gets even worse because of the lack of strictly separating borders. Think of a big forest. On one of its sides is town A (where you have the right of forestry), while on the other side lies town B, where I have the same right. Now we're in bad luck, because there is no obvious landmark in that forest (like a river) that can serve as a natural border. In that case you can get the impression (or just use that as a reason) that I am disrespecting your rights. Your rights on the other hand need to be shown to keep valid (not everything is written down, some things are shown often resulting in some kind of common knowledge). Luckily for you there is the right of feud to defend your other rights. The feud is the main violent conflict within the HRE. This conflict can not be kept up forever of course and was often solved through mediation (I won't describe the different processes here). The mediation can go many different ways, but for simplicity let's say the mediators find, that the whole forest should belong to you. So you don't need to share your rights in that one anymore and so to speak extended your borders of influence/rights. While the forest is a simple example, the most common point of conflict, that also resulted the most in the development of closed areas, were the law/court rights.

 

Did they function the same way the Schengen area/EU and you could live or work in any of the states or were they more closed of? Ok, this question can not be answered generally. The idea of every citizien within the EU/Schengen area being able to freely move, live and work within another of those doesn't apply to the HRE. The feudal system would not allow farmers to just switch places. If for example a man and woman from two close villages wanted to marry, it would require the agreement of the nobleman whose land their families are working and under whose court right they live. The development of (free) towns allowed some mobility, because it was possible to become citizen of or live in them, even though the person was technically dependent on a nobleman – a common conflict point between noblemen and towns. But you still would have to consider well if you want to change your place of living, because of the law system. Without finger prints and DNA-tests the defense if you are (wrongly) accused of a crime was usually asking witnesses. But not in the modern sense – they were not witnesses of the situation, but witnesses of you. They would have to testify under oath, that they know, you would never do whatever the accusation is and that you're an honest man who always speaks the truth. In a society that firmly believes in god no one who doesn't know in and out would take the risk of his salvation for testifying. Without such witness you are in a great risk of a god trial (wounding/burning and evaluation of the healing process). These risks are for example adressed in the jew privilege of Henry IV. From 1090.