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All I can tell you is that JPG export from ID has never been very good. Export to PDF, open that in Photoshop and save as JPG there.
BTW, if you really are using 7.0 then the first thing you should do is update to 7.0.4.
Commonly stated, InDesign is not very good at jpeg export. A better choice would be to export a pdf, open the pdf in Photoshop and save jpeg from there.
A 1 pixel line? That does not sound like a good idea, but I have never contemplated creating for monitors or web. If the line were not perfectly horizontal, I expect a break would occur or it would display poorly.
Pixelation on all pages - indicitive of broken links or change Display Performance to High Quality
The black line is physically in the exported jpeg and is not visible until the image is magnified severely or after printing.