Infinitesimal Unit of Measurement This is just a question that popped into my head which I lack the knowledge to answer (or even to know whether there is an answer, honestly). Does the idea of an infinitesimal unit of measurement even make sense theoretically? If I had a line segment, could it be of infinite length when measured in such units?

What mathematicians mean by 'infinitesimal' and how the word is commonly used are sometimes different. The common definition is that it is a quantity too small to be measured so the simple answer to your question is No. However, we could still ascribe values to sub-measureable quantities, see Could we assign a numerical value to an infinitesimal? And of course it's normal to leave infinitesimals as abstract values with certain properties resulting from their small magnitude. I can't help with your second question though.
