How should I check the assumption of linearity of the log-odds in a logistic regression and for multicollinearity when my predictors are all binary?

From what I've read, logistic regression assumes

1. $$y_i\sim \text{Bernoulli}(p)$$
2. $$y_i \perp y_j$$, for $$i\ne j$$ and $$i,j \in \lbrace 1,..., n\rbrace$$
3. log-odds is linear in $$X$$, i.e. $$\text{logit}(p)=X\beta$$
4. no multicollinearity among predictors
5. $$n$$ is large enough

However, I'm confused about assumptions 3 and 4 in the context where all my predictors are binary.

What plot or test should I run to assess if the linearity assumption is satisfied?

For multicollinearity, I know the way we define correlation matters. For instance, if your using ordinal data, Spearman correlation is appropriate. For nominal, polychoric correlation is appropriate. So, when doing a multicollinearity test, is it still reasonable to usual tests like VIF, condition numbers, and pair-wise correlation to evaluate multicollinearity? If not, what tools are appropriate? Would a pair-wise correlation with tetrachoric be appropriate? In the numerical case, I thought this was flawed because not all multicollinearity occurs just between pairs but can be groups of several predictors correlated with each other. Hence, VIF and condition numbers are used. Wouldn't this issue be present in binary data? If so, what is the binary equivalent of VIF and condition numbers?