Best Approach to Forecasting Numerical Value Based on time series and categorical data?
So the question is about to model the next repair date given the previous repairs.
If you have customer-specific data, where you have logged customer repairs to a specific customer, then it would be good idea to do time series, provided you have enough instances of customer repeatedly coming back.
If you have this scenario, then you can use something like an RNN (Recurrent Neural Network [https://towardsdatascience.com/understanding-rnn-and-lstm-f7cdf6dfc14e]) or LSTM, whereby you feed in the date time, type of damage at every time step to then get a single output date time.
If you have not logged a customer ID to the repairs to identify which repairs have been carried out for particular customers, then you could easily use a standard neural network for this.
Here you would train the model on all input data with the goal of getting a date time which equates to when the next repair is likely to happen.
In terms of data representation, you could represent the following features as the following:

Datetime: here, you could this as the day in the year, for example, Jan 1 could be represented as 1 and Dec 31 as 365. This can then be normalised (i.e. divided by 365) to reduce the scale of this feature.
Categorical variables like type of damage, etc: normally we represent these as one-hot encoded vectors (https://machinelearningmastery.com/why-one-hot-encode-data-in-machine-learning/).

To make the input for a given entry, we then concatenate these features into one massive vector.
Good luck!