Basically, the difference between 7...d6 8.a4 and 7...0-0 8.a4 is that Black can, in the first case, defend against the threat of axb5 by moving the bishop somewhere along the h3-c8 diagonal. He could also play ...Bb7, but then White will opt for d3 and the bishop will be inactive on b7.
Apart from 8...Bg4, 8...Bd7 is a common and decent move; in fact, in the similar line with 6.d3 instead of 6.Re1 it is the most common reply.

14.Nd2 allows 14...Bg5 or 15...Bg5, much more logical is 14.Qg3 or 14.Qg4 instead. White can play then 15.Be3 and 16.Nd2 for example. Rf1 and f4 is an idea, too.

So far as I can tell, Marin doesn't discuss your position after 13.d3 at all.  Nunn-Romanishin, London 1984 continued 13...Nd7 14.Nd2 Bg5! which looks like an immediate equalizer to me:



Overall Black seems absolutely fine the more I look at this, provided he's willing to sac a pawn with ...b5-b4! at the right time.

It's a move that's been tried a decent amount of times.  Besides transposing to the anti-Marshall lines, Black can play the immediate 8...Bg4.  Supposedly, having weakened the b4-square with 8.a4, Black is justified in giving up his light-squared bishop after 8...Bg4.  Marin paints a pretty rosy picture for Black of this line.

One key idea is the pawn sacrifice

where Black gets control of b4 and d4.  Of course, White is making a lot of pawn moves and Black plays for a lead in development. 

I suspect that White does better with 10.d3, though it doesn't exactly look fearsome, and indeed after some straightforward play like



Black seems to be very comfortable.