As for the http redirects the only solution I've found is rooting your phone and finding an adblocker.
It's tedious to unlock it when you actually need the store, but I seldom download apps so it's not a big deal.
If the button is not there it is likely that there is more than one file that you need or there are different options.
Once logged into the nexus site, go to the mod you want and click on the green button that says 'Download with NMM' (it's in the top right corner of the mod page).