Does the word "yas aluhu" here means to do dua and the meaning "we will attend to you" means Allah SWT will attend to your dua? Am I interpreting correctly here or no?
Your interpretation has some flaws, but let's first try to address each verse separately based on some sources:
As for ibn Kathir he considered the verse (55:29) as a part of verses in the same context and shows that Allah is ever living and rich and doesn't need any of His creation.
(Whosoever is in the heavens and on the earth begs of Him. Every day He is (engaged) in some affair.)
In this Ayah, Allah affirms that He is Rich, Free of all wants for anyone else and that all creatures stand in need of Him, in all conditions and situations. They all seek His help willingly or unwillingly. ... (Source qtafsir)
Imam al-Qurtobi in his tafsir -see here in Arabic- discusses a bit more who is asking and what they actually are asking:
The following translation(s) is(are) mine take it(them) carefully
(يسأله من في السماوات والأرض) قيل : المعنى يسأله من في السماوات الرحمة ، ومن في الأرض الرزق .
(Whoever is within the heavens and earth asks Him) it was said: the meaning is that those in heaven ask Him mercy and those on earth provision.
وقال ابن عباس وأبو صالح : أهل السماوات يسألونه المغفرة ولا يسألونه الرزق ، وأهل الأرض يسألونهما جميعا .
And ibn 'abbas and abu Salih said: Those in heaven ask him forgivness and don't ask him provision while those on earth ask Him both.
وقال ابن جريج : وتسأل الملائكة الرزق لأهل الأرض ، فكانت المسألتان جميعا من أهل السماء وأهل الأرض لأهل الأرض .
Ibn Jurayj added: and the angels ask Allah for provision for those (
the people) on earth, and this way both supplication have been made by those in heaven and those on earth for those on earth.
... وقال ابن عطاء : إنهم سألوه القوة على العبادة
And 'Ata' said: They asked Him the strength (power) for (being able to worship) worshiping.
He added a hadith which I couldn't find:
إن من الملائكة ملكا له أربعة أوجه ؛ وجه كوجه الإنسان وهو يسأل الله الرزق لبني آدم ، ووجه كوجه الأسد وهو يسأل الله الرزق للسباع ، ووجه كوجه الثور وهو يسأل الله الرزق للبهائم ، ووجه كوجه النسر وهو يسأل الله الرزق للطير
Allah has an angel with four faces, a face like that of a human, and this is asking Allah for provision for the sons of Adam (humans), a face like that of a lion and this is asking Allah for provision for the Siba' (lions and animals of that kind including dogs), a face like that of a bull and this is asking Allah for provision for animals, and a face like that of an eagle who asks Allah for provision for the birds.
In many tafsirs they also quote this hadith:
The Prophet said concerning the Verse: "Every day He is (engaged) in some affair." "His affairs include forgiving sins, relieving distress, raising some people and bringing others low." (Sunan ibn Majah)
so one could say your first interpretation goes along with the meaning expressed above.
As for (55:31) ibn Kathis quotes the following:
Ibn Jurayj said that the Ayah, (We shall attend to you,)
means, "We shall judge you," while Al-Bukhari said that it means, "We shall recompense you. Surely, nothing will busy Allah from attending to anything else." This type of speech pattern is common in the Arabic language. For example, one would say, "I will attend to you," even when one is not busy with anything else.
Allah's saying: (O you Thaqalan!)
refers to the humans and the Jinns, as in the Hadith; (Everyone will be able to hear it, except the Thaqalayn.(Sunan abi Dawod and Sahih al-Bukhari) In another narration that explains it, the Prophet said, (...except mankind and the Jinns.) (Source qtafsir)
This goes ahead with the context of the following verses (55:32-35)in which Allah is challenging both humans and jinn to seek a refuge from Allah's judgement and punishment.
Imam az-Zamakhshari in his al-Kashshaf -see here in Arabic- adds a connection to "Every day He is (engaged) in some affair." in verse 55:29 saying: that after their judgement the only affair that would be available is the recompense/punishment of these both kinds of His creation.
Imam at-Tabari make this clear by explaining the meaning that the judgement will lead to punishing the wrongdoers and recompensing does who have done well.
Note that "we will attend you" is a threat and menace! imam al-Qurtobi pointed at it referring to a statement from a lengthy hadith which is compiled by imam Ahmad in his Musnad (here in Arabic) and at-Tabarni in his al-Mo'jam al-Kabir (here in Arabic) and states a report of Ka'ab ibn Malik about the circumstances of bay'at al-'Aqaba as he witnessed them.
So this is the meaning on which the scholars are in consensus about is that this verse is a thread and reminder which is addressing the topic of judgement for both humans and jinn.