Am I able to give a second Hero's and Dungeon Handbook for rep?

On the same character I mean.

Yes. You may do as many as you like, but of course, you have to actually do at least half of the quests/dungeons over again.

As Kakumei said - but bear in mind: once you reach rank8 in a title track, only Hard Mode handbooks can be traded for more rep points on that title track.

Handbooks come with 5 of the quests already filled in - for some bizarre reason - so you can find the three quickest and easiest primaries in the game, do those, then trade in the book for 2k points and 400g.

Whether that's a good idea or not, I haven't decided...

couldn't you pay to fill it up completely and get 4k gold?

or is that just a 1 time deal?

As far as I know, the rewards stay the same. The problem is whether it's faster to do the same quests over and over to possibly gain rep points/gold more quickly or finish everything and get the max reward :P

One time deal, yep.