Questions regarding ordered probit model

I am currently working on a hypothetical research proposal for a course at my university. I am using data from three Afrobarometer surveys conducted in 34 African countries in the years 2011-2013, 2015 and 2019. I have to perform an ordered response model (i.e. ordered probit model) as my dependent variable comes from the following question:

Q26D: Here is a list of actions that people sometimes take as citizens when they are dissatisfied with government performance. For each of these, please tell me whether you, personally, have done any of these things during the past year. If not, would you do this if you had the chance: Refused to pay a tax or fee to the government.

With the answer possibilities ranging between: 0 = No, would never do this, 1 = No, but would do if I had the chance, 2 = Yes, once or twice, 3 = Yes, several times, 4 = Yes, often.

Until now, I came up with the regression displayed in the attached file. The X’s stand for my four explanatory variables coming from four different questions, the Z display added covariates for which I control, the D_t is a country-level dummy variable to control for heterogeneity across different countries and the α_t is a year fixed effect.

However, I am uncertain about the following points because this is the first time I am doing something like this:

1. Is the ordered probit model built up correctly the way I did it?

2. When looking at γ’Z_(i,t,c), do I have to specify the γ with a subscript as I have 12 different control variables I am looking at, i.e having a notation like γ_k’Z_(i,t,c)? And do I have to transpose the γ such that γ’Z_(i,t,c) or don’t I have to use a transpose such that γZ_(i,t,c)?

3. A just have a repeated cross-section dataset and not a panel dataset. Nevertheless, is it right to have the subscripts (i,t,c), or should I just account for (t,c) as I am not looking at the same individual in each of the three surveys because different individuals were asked in each survey?

4. My control variable accounts for the respondants’ age (Q1), mother tongue (Q2A), occupation (Q95A), religiosity (Q98), education (Q97), gender (Q101) and race (Q102) as well as the respondents’ present economic situation (Q4A), present living condition (Q4B), their free speech (Q14), satisfactory with democracy (Q36) and covariate to control for corruption (Q44D). However, now I am wondering if I can control for mother tongue, religiosity, gender and race in the way I am doing it because these variables are time-invariant and would drop out when applying year fixed effects α_t? Am I running into some problem here? How should I account for this? I want to urgently show which direct effect mother tongue, religiosity, gender and race have on the dependent variable, but is this possible with year fixed effects?

I really hope that you can help me!

Thanks to everyone!

[built-up ordered probit model] [1]: https://i.stack.imgur.com/86jlC.png