Naruto Shippuuden Episode 342

[DarthEnderX]

Tobi doesn't even use his advanced Sharingan version, he can do his stuff without using the MS

Do you have any proof of that? They've never shown his Sharingan WHILE he's used his dimensional powers before.

Itachi's MS isn't his own either, he got one eye from a friend (see flashback)
if I'm not mistaken, his own MS is that special illusion-jutsu

The one he got in the flashback is the one he implanted in the crow that he stuck inside Naruto(notice how it looks nothing like Itachi's MS).

Itachi's MS is:
Right Eye: Amaterasu
Left Eye: Tsukiyomi
Both: Susano'o

Shisui's MS is:
Right Eye (which Danzo stole): Koto Amatsukami
Left Eye (which he gave to Itachi): Koto Amatsukami

And just to save time...

Sasuke's MS:
Right Eye: Inferno Style - Flame Control
Left Eye: Amaterasu
Both: Susano'o

Ubito's MS:
Right Eye (being used by Tobi): Dimensional-jutsu that's slightly different than Kamui.
Left Eye (given to Kakashi): Kamui

Madara's MS:
Right Eye: ?
Left Eye: ?
Both: Susano'o

and I wonder why Tobi has the Rinnegan(?) if he is not really going to use it, or did he just grab it to get knowledge about the techniques he required

He did use it, to control his 6 Pains. And presumably the Rinnegan is also what allowed him to summon and control the statue.

But you're right, he's wasting a lot of it's powers. He's not using the Almighty Push, or the Jutsu absorbtion or any of the other shit it does.

Kakashi gave the excuse before that channeling the tailed beast energy to his Pains must have been using too much concentration for them to use the other Rinnegan powers, but now that they're gone, there's no reason he shouldn't be using the Rinnegan powers himself.