For short templates I agree that there should be natural and ddNTP termination both giving a full length product. If this cannot be seen then possibly the gel composition is set to distinguish the lower range of sequences....eg 30-300 bases and it may be that the full length signal is poorly separated and only just runs out of the wells because it is outside the effective range of the gel. Possibly also the mix is too depleted for the longer sequences and all of the labelled primer has been used in generating the short sequences indicating not enough primer or too much template.
If your template dna is very long then either the polymerase falls off or the reagents become depleted so ther might not be enough reagent mix to show the longer extensions
The exact ratio of ddNTPs to dNTPs can influence how long a new DNA molecule you can get. More dNTPs means longer strands (on average). But there is an upper limit of how long a sequence you can make before the polymerase uses a ddNTP.
Yes, you will get many copies of new DNA with terminator bases at the exact same location. That's how the signal is "bright enough" to be read by the laser.
The reason you don't see a "band" is that standard agarose gel electrophoresis simply does not have that sort of resolving power. Lined up by size, each type of molecule is exactly 1 nucleotide longer than the next. That's why you use a capillary tube for Sanger - the DNA molecules are separated by size & the resolution is to single nucleotide differences. Pretty amazing really!
Take a look at an older molecular biology textbook and it will talk you through more of the details.
Note: most folks now mean "4 fluorescent labeled ddNTPs in capillary tubes, single reaction" when referring to Sanger. Originally, you set up 4 separate reaction, used isotope-labeled dTNPs (one with dATP, one with dCTP, etc) and used an acrylamide sequencing gel to run out the samples side by side to learn the sequence. I don't think anyone uses that method, or has for years, but it's good to know the history.