Is this the correct way to use the nick property? And a good multiclass?

So I'm playing a vl 7 way of shadow monk, 5.5e. Up until this point, I've done nothing but unarmed strikes, however we have a level up coming up (2 per year) and I'm starting to think about a possible multiclass.

In my digging, I saw the monk/fighter combo, which looks really tempting. (Mainly for action surge.) But that led me to seeing ways to get about 8 attacks in one turn, using the attack action + extra attack + nick property on a dagger, bonus action for 2 more (3 once I reach I think lvl 10 or smth monk), action surge for two more attacks since nick is once per turn.

I'm certain that's correct, except for nick. This monk is the only 5.5 character I've played, so i haven't used weapon propertly things literally at all. Is that the correct way to use nick? COuld i have been getting three attacks every time I take the attack action?!

please advise. And if you hve any tips or suggestions regarding the multiclassing, please advise.

You have that right. At a minimum of Fighter 2/Monk 11 you could make 8 attacks: 3 with your first Attack action thanks to Nick, Action surge then the Attack action again for 2 more, then Flurry of Blows for 3 more. I have seen this done with a Bugbear Monk to get an extra 2d6 on each attack during the first round, and it can make for a pretty banger nova round. It works really well on a Warrior of the Open Hand if you use Flurry of Blows first to knock them Prone so you can have Advantage on all your attacks after you do.