Binary predicting time series I have a time series dataset as follows (just 1 part out of 1000 obs). The data includes only the time and the outcome (1 - success, 0 - failure). Time here is not the amount of time but the date (For example, test 1 is performed at 15:18:56 on 10/9/2012, not that it took 15 hours to complete).
Tests are independent but it is assumed that lessons learned after a failure

Questions:
(1) Do you know any package in R/ Python that could help predicting this data?
(2) How the assumption of lesson learned impact the prediction model?
 A: You might consider the model 
\begin{align*}
y_t \mid x_t &\sim \text{Bernoulli}\left(p = \frac{e^{x_t}}{1+e^{x_t}}\right) \\
x_t - \mu  &= \phi( x_{t-1} - \mu) + w_t
\end{align*}
where $y_t$ is your $0,1$ observation and $x_t$ is some hidden state. I think the KFAS package can handle this, but I've never used it. That vignette also mentions other software that you can use for this model.
It's  kind of a fancy model, but if you can figure it out, you'll be able to see how the probability of a $1$ changes over time in different ways.
A: If you want to predict the outcome based on time, where outcome is your response try using survival analysis. Your data looks like a good candidate for this analysis. 
Survival regression model and Kaplan-maier estimate (probability function) are available in R. The pakage is survival. Here is a link to a good tutorial.
https://www.r-bloggers.com/survival-analysis-with-r/amp/
A: I've used a multi-order markov transition table with reasonable success in the past.  This should capture the possible learning after a failure to some extent.  It should be pretty easy to port this Matlab code to R or Python.
Multi-Order Markov Transition Table
Perhaps this R package does a good job of fitting high order transition tables:
MarkovChain package
