Soul Contractors can use their soul's power but they can't only depend on it you need a fundamental combat skill to use it further plus soul contractors use a mana 

Mana is one of the fundamentals because you used it to use your soul ability like fire In Suzuya and Akane's case 

While Suzuya and Akane's ability is elemental Yasha's Chain Manipulation means he can control chains and produce them while in combat 

Soul Contractor Can act alone even if your soul is not with you like Yasha did when he fight Suzuya he didn't bring Chikako along with him 

The Price of being a Soul Contractor depends on a soul because they are the ones the decide what they want from the people with whom they formed a contract 

Plus Soul Contractor can evolve while they more interact with each other and cooperation is the key here 

Back to the mana if you ran out of mana you can't use the ability of your soul and you can feel your body getting exhausted. 

Mana can be used in different ways 

The soul can come in any form to come in contact with its possible contractor for example in Akane's case is an orb but we don't know about the others.

The eye of the user changes colors when using their powers.

Soul Link is like communication. But it's happening in the Soul Contractors' minds they can only talk for a few minutes depending on their mana capacity. And another condition is the Contractor must be in a nearby location and fine.