Assalaamu alaykum. I would like to know about the supplications mentioned below whether reciting them is allowed or not in the light of the Quran and Sunnah:
1. Allahumma ya wadudu azal arshil majidi ya mubdiu ya mueedu ya fa alunllimayuridu azal izzatillati laturamu walmukil llazi la yuzamu yaman ala nurihi arkana arshihi ya mughisu aghisni ya mughisu aghisni ya mughisu aghisni innaka alakulli shainn qadeer.
2. Ya rajayi ya manai ya dawayi ya shifayi ya kafayi kafiyun yuhyi ya ghafuru ya ghafuru ighfirli qati ati yauma yubasuna ya allahu ya allahu ya allahu ya rahmanu ya rahmanu ya rahmanu ya rahimu ya rahimu ya rahimu ya ghafuru ya ghafuru ya ghafuru ya karimu ya karimu ya karimu wasallallahu ala khari khalqihi wanuri arshihi mohammadiyun wa alihi wa ashabihi ajmain bi rahmatika ya arhamarrahimeen.
Souce: Pakistani Panjsurah

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

It is permissible to recite the first supplication, and may Allah respond to the one who supplicates Him with it. What is better than this is the supplication of distress: "La ilaaha illa Allah al-Haleem al-‘Atheem; La ilaaha illa Allah rabbu-l-‘arshi-l-kareem, La ilaaha illa Allah rabbu-s-samaawaati as-sab‘i wa rabbu-l-‘arshi al-‘Atheem. (There is no god (worthy of worship) but Allah, the Forbearing, the Great; there is no god (worthy of worship) but the Lord of the Noble Throne, there is no god (worthy of worship) but Allah, the Lord of the seven heavens and the Lord of the Great Throne.)"

Another great supplication is that of Prophet Yoonus (Jonah) : "La ilaaha illa anta subhaanaka inni kuntu mina-ath-thaalimeen." (None has the right to be worshiped except You, indeed I was among the wrongdoers) There is no one in distress who supplicates Allah with this supplication but that Allah responds to him.

As regards the second supplication, it is not permissible to supplicate with it because it includes the phrase "ya dawaa’i," which describes Allah as dawaa’ (medicine); a matter that is neither confirmed in a hadeeth nor in a statement of the Companions; rather, it is confirmed that Allah is the Tabeeb (the real curer), as mentioned in the hadeeth of Abu Ramthah who said to the Prophet “Show me this thing on your back as I am a doctor.” Thereupon, the Prophet said to him, “It is Allah Who is the Tabeeb; rather, you are a kind man. Its Tabeeb is the One Who created it.” [Abu Daawood and Ahmad; Ahmad Shaakir and Al-Albaani classified it as saheeh (sound)]

Moreover, the second supplication includes the phrase "wanuri arshihi muhammad", which means that the light of the Throne of Allah is Muhammad . This is also neither confirmed in the Quran nor in the Sunnah.

The Fatwa of the Permanent Committee of Iftaa’ reads, “It is neither confirmed in the Quran nor in the authentic Sunnah that Muhammad is the light of the Throne of Allah. So whoever claims this is a liar.”

Therefore, our advice to you, dear brother, is to supplicate with the authentic supplication that were mentioned in the Quran and reported in the Sunnah, as there is much goodness and blessings in them in this world and in the Hereafter, and to avoid supplicating with any invented supplication, as this is dispraised Islamically.

It was reported that Sa’d heard his son supplicating, "O Allah, I ask You for Paradise and its delights and its brocade and the like, and I seek refuge in You from Hellfire and its shackles and its chain." Thereupon, Sa’d said to him, "Indeed, you have asked Allah for much goodness and you sought refuge with Him from much evil, and I have indeed heard the Prophet say, 'There will be people who will transgress in supplication, and then he recited this verse (which means): {Call upon your Lord in humility and privately; indeed, He does not like transgressors.} [Quran 7:55] It is enough for you to say, ‘O Allah, I ask You for Paradise and for what brings one closer to it of words and deeds, and I seek refuge in You from Hell and from what brings one closer to it in words and deeds.’'" [Ahmad in Al-Musnad]

Allah knows best.