Hello. Some quick notes that could be expanded...

Q1. Yes, there's really no real cutoff above which the distribution of the estimated parameters in a parametric analysis is guaranteed to be approximately normal. 30 won't cut it in all cases, and probably shouldn't be discussed like it's a magic cutoff. 100 in a group is better.

I really think it's best to either understand you data (Is it expected to be approximately conditionally normal?) or just look at the residuals from the analysis.

Q2. Levene's test is a test for equality of variances among groups. A significant result suggests that the test is able to detect heterogeneity of variance. Since you have a large sample size, the test probably has the power to detect relatively small differences in variances.

Q3. I don't recommend ever running tests for homogeneity or normality as a precondition for running e.g. anova. I would like $1 from every instructor per student that they've recommended this approach.

Instead, plot the model residuals against the predicted values. Or, in a one-way design, look at the variances within each group. What counts as too heteroscedastic? I don't know. But I'm sure you could find some general guidance.

Q4. Yes. In a one-way design you could use Welch's anova. In that or other designs, you could use weighted regression, or sometimes adjustments can be made to the degrees of freedom for hypothesis tests, like in R you can use White adjustment.

Q5. Dunno. If the other variables don't matter, there may be no reason to include them.

I recommend you read some of the chapters in the book below. Good luck

https://www.pearson.com/us/higher-education/program/Tabachnick-Using-Multivariate-Statistics-7th-Edition/PGM2458367.html

I'll add one point to the thorough response you got from Salvatore. The following is an excerpt from the 1997 edition of the late David Howell's popular textbook, with emphasis added.

"In general, if the populations can be assumed to be symmetric, or at least similar in shape (e.g., all negatively skewed), and if the largest [sample] variance is no more than four times the smallest, the analysis of variance is most likely to be valid. It is important to note, however, that heterogeneity of variance and unequal sample sizes do not mix." Howell (1997, p.321)

With n1= 100 and n2 = 400, I would very inclined to use a test that does not require homogeneity of variance almost without even looking at the variances. Some people--e.g., Daniel Lakens-- recommend using such tests all the time--see the article link below. I think that is too wasteful of power when the sample sizes are equal or nearly so. As George Box noted, when sample sizes are all the same or nearly so, one can almost ignore variance heterogeneity. The attached image has a quote from one of Box's articles that addresses this point, as well as normality. HTH.

Article Why Psychologists Should by Default Use Welch’s t-test Inste...