Is it permissible to sit in the mosque immediately upon the call to prayer (adhan) if standing is difficult for the worshipper, and then perform Tahiyyat al-Masjid (greeting of the mosque) after the adhan has ended?

It is permissible to perform 'Tahiyat al-Masjid' (two rak'ahs upon entering the mosque) during the Adhan, though it is preferable to follow the Mu'adhdhin (the caller to prayer). As for sitting before performing 'Tahiyat al-Masjid', the prohibition is for Tanzih Karaha (disliked but not forbidden) and not for Hurmah (prohibition).