Is it permissible to work as a muezzin with the intention of remaining steadfast in religion and maintaining congregational prayers, along with the intention of securing a monthly income and housing that facilitates marriage, and does the presence of the second intention affect the primary intention?

If the Adhan (definition) is compensated from the public treasury (Bayt al-Mal) or endowments (Awqaf), there is no harm in that, because it meets a need of the Muslims and prevents its cessation. However, if the payment comes from an individual or a group, it is preferable to avoid the difference of opinion, due to the prohibition against taking wages for the Adhan, unless you are poor and in need. In that case, it is permissible for you to take it, and this does not detract from your original intention, and you will be rewarded for it.