Yes, there are answers to Shri Madhwacharya's Mayavada Khandana and Upadhi Khandana given by Advaita scholars.
For example, in the Vakyartha vidwat sadas of the Sringeri Sharada Peetham held every year, scholars debate various philosophies and discuss why Advaita is tenable. In 2008, the refutation of Mayavada Khandana was provided. See the site containing the set of papers.
The fourth paper is मायावादखण्डननिरासः — विद्वान् के.पि. बाबुदासः, कालटी presented by K.P. Babudas of Kalady.
Similarly, in 2011, in the vidwat sadas, he refuted the work Shri Madhwacharya's Tattvodyota.
All major works of Dvaita have been refuted by Advaita scholars and Gurus. However, the primary source of Dvaita is the Nyāyāmṛtam of Sri Vyāsatīrtha. Sri Madhusudana Saraswati, the author of the Advaita siddhi and its commentator Brahmananda Saraswati have done monumental work in refuting the philosophy of Nyāyāmṛtam and given the arguments of Advaita.
Your primary question is If Brahman is Self luminous, why does Maya cover it? anAdi mAyA and samsara are not within the gamut of logic. Advaita holds all this ‘anirvachanIya’. Two answers can be provided: From the paramarthika point of view, Brahman was always luminous and there was no avidya at all. From the vyavaharika point, avidya is to be removed, then it will be realized that Brahman was always Self luminous.
Tirodhaanaanupapatti – logical inconsistency in regard to obscuration (aavaranam).
Objection: Avidya obscures Brahman which is eternal self-effulgence amounts to saying that the nature of Brahman is destroyed.
Refutation: The obscuration (tirodhaanai) is in the form of jiva’s non-apprehension of jiva himself being Brahman. This non-apprehension does not affect Brahman just like the formation of a cloud hiding the sun cannot be attributed to the sun.
Atma Bodha is very clear on this
parichChinna ivAj~nAnAttannAshe sati kevalaH |
avachChinna svayaM prakAshate hyAtmA meghApAye.n.ashumAniva || 4||
Due to Ajnana (ignorance), one imposes limits to Atma. When this Ajnana is
destroyed, Atma can be visualised just as sun appears emerging when dark clouds are dispersed.
Verse 17 of advaitamakaranda is similar:
tathApyAbhAti ko.apyeSha vichArAbhAvajIvanaH .
avashyAyashchidAkAshe vichArArkodayAvadhiH .. 17..
This inexplicable ignorance appears in the absence of enquiry. It is like thick mist in the space of Consciousness that lasts till the rise of the sun of Knowledge, born of enquiry.
As the true nature of sun appears to be hidden by a cloud, the true nature of the eternal and self-luminous Atma is hidden by ignorance. This ignorance can be only destroyed by knowledge, arising due to realisation.
Regarding the upadhi, from Atma Bodha
dehendriyaguNaankarmaaNyamale sachchidaatmani .
adhyasyantyavivekena gagane niilataadivat.h .. 21..
Due to lack of discrimination, people superimpose on the Atman [which is the Absolute-Existence-Knowledge (Sat-Chit)] all the varied functions of the body and the senses. This is just as they attribute blue color to the sky.
Sky is not blue but appears so. Due to lack of discrimination, upadhis are superimposed on Brahman.
aGYaanaanmaanasopaadheH kartutvaadiini chaatmani .
kalpyante.ambugate chandre chalanaadi yathaambhasaH . 22..
The doership of action, enjoyment and other limitations really belong only to the mind but are understood to be the nature of the Atman due to delusion. This is like attributing the trembling of the moon reflected in the water to the moon and not to the water.
The ring is a name for Gold in that form (vAchArambhaNa) and is called upadhi of gold. Even though gold is identified in the form of ring, the form itself will not affect gold. The knowledge of gold is not influenced by the ring and is same as derived from ring, bracelet or necklace. The ring, - which is not a part of gold, but used to identify gold - is called the upAdhi of gold.
Shankara makes this statement in his Brahma sutra bhasya:
upAdhi, though attached to object, is not attached; upAdhi though appears to be in object, is not in object.
The names and forms of jagat are upAdhis for Brahman. Though Brahman may be identified by its upAdhis, it is unaffected by it just like gold is unaffected by the ring or bracelet.
In the Gita Bhasya of Shankara, the declaration of Krishna in gIta
mat sthAni sarva bhUtAni na cha aham tEshu avasthitah 9.4
Though all beings are in Me, I am not placed in them. Thus jagat itself is a upAdhi of Brahman. Gold is in all rings but change of form from ring to bracelet does not affect the gold.
Thus, according to Shankara, Brahman is the abhinna nimitta (undifferentiated material) as well as upAdAna kAraNa (intelligent cause) of the jagat.