1) How many indicator variables can be included in the model?
2) Is there a relationship that should be considered between sample size and parameters to estimate?
3) Having achieved the probability of belonging to each class of individuals, there is a cutoff point that could be used? For example, if the probability of the subject 1 is = Class 1: 0.20 Class 2: 0.40 Class 3: 0.40 Class 4: 0.20 Should consider this case for further analysis? Is there some literature on this point?
2) Your sample size should be considerably larger than your number of parameters. To be more precise about the sample size needed, you have to do a Monte Carlo study.
1) It is easy computationally do handle at least 100, but see answer to 2)
3) Your example is a person with poorly determined class membership. You should strive for at least 0.80 in one class. But in terms of relating the latent class variable to other variables, you don't have to use this multi-step, analyze-classify-analyze approach, but do it in one step. There will shortly be a paper posted on this topic.