> Note that Sigurð <féll> 'fell', but Brján <fell> 'falls'.

Both past tense, I think. Vowel length is hardly ever marked consistently in the manuscripts. Editors who use more archaic normalised spelling give the past tense with short <e>, <fell>, <fellu> 'fell', whereas Zoega has the more modern spelling <féll>, <féllu>. The third person present singular indicative would be <fellr>, as assimilation of <r> to a preceding single <l> happened when the vowel before the <l> was long, but <r> wasn't assimilated to a preceding <ll> (Gordon, § 76), e.g. in <fullr>, <allr>.

This verse with archaic normalised spelling:
http://notendur.hi.is/~eybjorn/ugm/skindex/xidr03.html
http://skaldic.arts.usyd.edu.au/db.php?table=verses&id=1323

And more generally:
http://www.septentrionalia.net/lex/index2.php?book=e&page=120&ext=png