In his book, De Inventione (and also De Natura Deorum), Cicero discusses the process of rational thought and he generally uses the word ratio to mean reason as an abstract process. For example,
Ac me quidem diu cogitantem ratio ipsa in hanc potissimum sententiam ducit, ut existimem sapientiam sine eloquentia parum prodesse civitatibus, eloquentiam vero sine sapientia nimium obesse plerumque, prodesse nunquam.
(For my own part, after long thought, I have been led by reason itself to hold this opinion first and foremost, that wisdom without eloquence does too little for the good of states, but that eloquence without wisdom is generally highly disadvantageous and is never helpful.) H. M. Hubbell trans.
So, he uses the term ratio ispa (reason itself). So, ratio can be in Latin, as in English, both "a reason" and "reason itself". This use was consistent throughout history. For example, Boethius (480-523) in the De consolatione philosophiae uses the same expression, ratio ipsa.
Another example can be found the letters of Seneca when he compares the thinking of animals to that of humans:
Quid in homine proprium? Ratio. (What is the distinguishing characteristic of man? Reason.)
To answer your second question, the Romans did directly equate λóγος with ratio. For example, from Cicero's De Fato:
Nec nos impediet illa ignava ratio quae dicitur; appellatur enim quidam a philosophis ἀ⍴γòς λóγος, cui si pareamus nihil omnino agamus in vita.
(Nor shall we for our part be hampered by what is called the ‘idle argument' for one argument is named by the philosophers the Argos Logos, because if we yielded to it we should live a life of absolute inaction)
To answer your third question, there is no other word that commonly means reason itself, other than ratio. The word causa can mean "a reason," but is not normally used to mean the process of reasoning. There is a word ratiocinatio which refers to reasoning in a scientific sense, such as a syllogism:
Ratiocinatio est oratio ex ipsa re probabile aliquid eliciens quod expositum et per se cognitum sua se vi et ratione confirmet.
(Deduction or syllogistic reasoning is a form of argument which draws a probable conclusion from the fact under consideration itself; when this probable conclusion is set forth and recognized by itself it proves itself by its own import and reasoning.)