> Og síðan bjó hann þar eftir föður sinn.
> And afterwards he lived there (in memory of?) his father.

Simply: "And then lived (continued living there) there after his
father('s death)".

> og keypti skip að honum
> and bought a ship of him? (or for him?)

"off/from him". Z 'at' IV. 8 "determining the source from which
anything comes".

> hálfur fjórði tugur manna
> 35 (Z) men

That's right; well done! It's a tricky and counterintuitive idiom for
us English speakers. It reminds me of the way Icelandic, like German,
counts the time half way to the next hour, whereas English counts half
hours past the previous hour.

klukkan hálf níu = halb neun = half (past) eight


> I have read both that the Vikings never cooked onboard ships and
also that they did cook over the ballast which was probably sloshing
with water at the bottom so fairly safe if the weather wasn't so bad
the sail would catch fire.

Interesting. I can't call to mind any examples from sagas one way or
the other. That's something we'll have to look for. I saw a
documentary a couple of years ago about an attempt to row a
reconstructed viking ship across the North Sea, but they had their
meals in ingenious, modern, self-heating packaging...