I think you can just build binary classifiers to build your discrete-time survival model: https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-022-01679-6
See especially the discussion around figure 1) to understand how you need to resample your data for a discrete-time survival model
This approach is super flexible. I miss the discussion of discrete-time survival models a lot! For a calibrated classifier the predicted score is the hazard probability in a given time interval.
Additionally proper scoring rules and the evaluation metrics of a binary classifier help you judge your model's predictive performance (on hold out test sets)
For your question A) yes: if you know your samples are not drawn according to the population distribution (but are oversampled), you could take care of this when constructing the training set for the classifier - you would then draw samples from the oversampled survival times less frequently.
Some main take-aways from the paper of Krithika Suresh, Cameron Severn & Debashis Ghosh:
"Note that we do not make the assumption that the event indicators within a subject are independent and have a binomial distribution. Instead, we observe that the likelihood function for the discrete-time survival model under non-informative censoring can be represented using a binomial likelihood that assumes independent event indicators"
"Due to the binomial structure of the likelihood function in Eq. (2) the discrete survival time formulation is general and any algorithm that can optimize a binomial log-likelihood can be used to obtain parameter estimates. Thus, within this approach we can apply any method for computing the probability of a binary event and can choose from various binary classification methods, from traditional regression methods to more complex machine learning approaches."