Could Nikah or Muta ever be not mustahab, or even makruh or haram like in the case of one not earning enough income? Or worse if one has history of brain/psych/or/spiritual diseases?

Also, is it lack of eeman that makes it seem like a hurdle or common sense to just have steady cash first? Also/then, and what would be the better first step if is indeed determined still mustahab even in straighened circumstances (i.e. seek earnings firstly, independent housing first, or just socialize to pursue marriage firstlly)

Yes although Nikah is one of the most recommended act in Islam and best Sunnah of Holy Prophet (saww) but same time if anyone has such aforementioned diseases or disorder then even if he/she has done Nikah after that his/her spouse has complete right to separate without divorce and Nikah will be nullified automatically.
But as for as having job or life necessities concern here Islam says : in chapter Noor Ayah 32

وَأَنكِحُوا الْأَيَامَىٰ مِنكُمْ وَالصَّالِحِينَ مِنْ عِبَادِكُمْ وَإِمَائِكُمْ إِن يَكُونُوا فُقَرَاءَ يُغْنِهِمُ اللَّهُ مِن فَضْلِهِ وَاللَّهُ وَاسِعٌ عَلِيمٌ

And marry those among you who are single and those who are fit among your male slaves and your female slaves; if they are needy, Allah will make them free from want out of His grace; and Allah is Ample-giving, Knowing.(An Noor:32)

Here we should give priority to save our modesty over our economic condition also in many affairs of our life, we have no role. Many times we plan nicely and try our level best but do not achieve the goal according to our plan. Therefore many affairs we should hand over to Allah and we should try only. As Quran says in Surah Najm

وَأَن لَّيْسَ لِلْإِنسَانِ إِلَّا مَا سَعَىٰ

And that man shall have nothing but what he strives for- (53:39)

We have hundred and thousand examples from pre Islamic era till now where at the time of marriage many men have nothing but relying on Allah they saved their modesty and spirituality then Allah blessed them lots example of Prophet Yūsuf (a.s) from slavery and prison at last he became the King of Egypt. Imam Ali (a.s) at the moment of his marriage had just one piece of Armor and he sold that but didn’t extend his marriage. So we should not worry about that but yes even if anyone has no such disease that can not going to affect his marital life he has right to get marry but ofcourse for mad or any mental disorder person it not good if they can’t run their life smoothly.