Agreed.
Sorry, but no help from the outside.
I know, but to mark him Minato has to reach him first and Kakuzu could make a hand sign in that time. Not knowing about Kakuzu's hearts is a serious disadvantage. Kakashi caught him off guard with a Raikiri in the back and almost died because of it. Minato would have to kill him 5 times and there's no way to find that out unless he tells you. Plus, Kakuzu tricked Kakashi even thought Kakashi has a dojutsu such as a Sharingan. If he marks him and starts teleporting to Kakuzu, it would take a fair amount of Rasengan to break his skin and Kakuzu won't allow that. He would predict where Minato would appear (next to him) and strike with his threads
The thing is, Kakuzu will block minato's initial flurries. He may tank a rasengan, kill some toads, dodge some kunai, what ever. But, eventually he'd get marked. When that happens (he won't notice, no one does), minato 'kills' him. Now, minato thinks he's dead, but then kakuzu gets back up. Minato wonders whats going on and eventually he'll see the masks and that one is broken (either kakuzu goes earth grudge, or he releases the masks) but basically he'd notice a broken mask. If the masks were out and he killed kakuzu, he'd notice a mask going into kakuzu reviving him, then breaking. We know minato is smart. Right there he'd notice something isn't right and wonder what's going on. Kakuzu is already marked, and unless he sits entire fight with domu active(he won't be able to move at all), minato will kill him again. Minato will find the link between masks and lives, and it will only be a matter of time before kakuzu dies.
The biggest thing is minato has an arsenal of nature, barrier and sealing techniques we have never seen. That will work in his favour to beating kakuzu. That and the fact that minato is a bigger mystery that kakuzu. Kakuzu's only mystery is domu and his hearts. Minato has FTG, barrier techs, sealing techs that mostly no ninja know about.
Infact, kakuzu would most likely lose his first heart from a flying kunai. Knowing about FTG isn't knowing about FTG2. He'd see minato teleporting to kunai and make that link. Minato would probably try a rasengan on him (because minato is quicker than him and wouldn't need to resort to FTG2 to do something like that initially), kakuzu will use domu and minato would learn that secret. Then, minato throws a kunai, kakuzu dodges it or, worse yet, deflects it thinking it's just minato tossing his kunai as a diversion, but then minato would use FTG2 and kakuzu wouldn't have time to react and use domu. Obito didn't evenhave time. From there, kakuzu has lost 1 heart, and he's marked. Unless kakuzu starts with full info on minato (pretty much impossible unless minato hands you a handbook on 'how to defeat me. Secrets of all my jutsu), kakuzu would be fighting in the blind.
Remember, everyone we've seen minato fight didn't know about;
FTG2
his ability to mark with just a touch
Infact, bee probably didn't even know he would have teleported to the kunai. He probably just saw minato appear and retaliated quickly.
EDIT: Also, FTG barrier can pose a serious threat to kakuzu. Minato could possibly redirect flash darkness back to him. He'd be dead right there since domu can't tank that.
Minato could potentially take out three of kakuzu's hearts in a flash.
FTG2
Marked FTG blitz
Redirected flash darkness.
From there kakuzu has to be extremely careful.