Since a philosopher exercises his philosophy speaking and writing, is philosophy constrained by the limits of the language?
No, a philosophy is constrained by the limit of thinking. A philosophy is based on meditating, asking questions to yourself, wondering, finding explanations(or at least look for them).
And if the language restricts you to write your thoughts, only then, yes, the language becomes a limit.
Here you can find what is the philosophy and mainly, the only limit, is you.
The reply needs to be nuanced. Probably more nuanced than I can manage but I will try to walk carefully through a minefield. In a word, philosophy is constrained by a philosopher's language.
▻ A COMMON WORLD : CO-REFERENTIALITY
Not totally. There are respects in which all language-speakers share a common world to which at least some of their assertions refer. The associations (beliefs about the referents : the 'sense' as I shall call it later) may be different but all languages have words which refer to the sun, the moon, to shadows, to distance, to space, to time, to succession and simultaneity, to past, present and future. In the lingo the words are co-referential.
▻ SENSE VERSUS REFERENCE
But other examples unsettle the simple picture. 'The Shoah' and 'the Holocaust' are co-referential - they refer to the same event - but the sense or meaning of these terms is different between Hebrew and English speakers. They can't be said, without more ado, to mean the same. A non-Hebrew-speaking English philosopher cannot think about the Shoah in exactly the ways a Hebrew-speaker can. A barrier of different sense comes down sharply between them.
▻ LINGUISTIC INCOMMENSURABILITY
Each culture is likely to have concepts that are specific to it and in some cases cannot be understood in another language. This isn't the Shoah point repeated. There is a common reference if a different sense between 'Shoah' and 'Holocaust'. But if you take the English term 'moral rights', there is no precise equivalent to this expression in Ancient Greek : there is no common reference. The same, I suspect, is the case with 'duties'. The Ancient Greek moral conceptual scheme did not operate with these notions, not exactly these notions. There are moral reflections an Ancient Greek could not have had because there was no language (either in direct terms or by circumlocution) in which to think about them. The same is true in reverse with Ancient Greek terms such as eudaimonia, diakaiosune, moira. We can approximate these terms in English but only by thinking in Classical Greek can we fully comprehend them : which means that the limits of English set limits to what we can think. Only by stepping into the conceptual scheme of another language can we escape the conceptual constraints of English.