Well, first off...Your test of the battery only revealed half of it....
If it metered above 12 volts with engine off, then it should try to crank and all lights and accessories shoud work....12.8 volts is considered fully charged with engine off, but that's only half of it.
You had no business buying alternator before you started engine and retested battery...even if you had to jump it to start it, you should have then tested batt voltage again with it running even if you had to gas it to keep it running before buying alternator...So stop spendiong money swapping parts until you do some follw up testing.
Once running, even if you had to jump it, the readings across the batt terminals (in the center of the posts, not at terminal clamps) should meter out well above 13 VDC, up to 14.5.
If you get well above 13 VAC at center of batt terminals with engine running, then alternator is working and battery terminal clamps are tite and clean unfuff to recharge battery and start it.....If not, then shift meter probes to battery cable clamps...if the battery cable clamps show above 13VAC, then clean and tighten clamps where they attach to battery posts and if they or one is a temporary style clamp, then toss it and reattach new new clamp after cleaning and brushing cable wires to shiny clean.
There's more, but do that first