To make a predictive model, you will first want to split your data into train and test sets. You can then use the training data to try random forest, regression, gradient boosting, and parametric survival regression models.

In R:

library(randomForest)
library(gbm)
library(caret)
library(survival)

set.seed(22)

survival = read.csv('survival.csv')

rf.model = randomForest(OS ~ . - Patient - Death, data = survival)
varImp(rf.model)

reg.model = glm(OS ~ . - Patient - Death, data = survival)
varImp(reg.model)

gbm.model = gbm(OS ~ . - Patient - Death, data = survival, n.minobsinnode = 1)
summary.gbm(gbm.model)

surv.model = survreg(Surv(OS) ~ . - Patient - Death, data = survival)
summary(surv.model)

Note that I excluded Patient and Death from the OS model since Patient is irrelevant to OS and Death is too similar. You just want to use gene expression to predict survival. You can use the same methods to predict Death, just indicate family = 'binomial' in the glm model. In that case, you will want to exclude OS from the model. n.minobsinnode in the gbm model will probably need to be optimized.

Once you have your models, you can use the test data to make predictions, which you can then compare to the actual values. You can use error (e.g. root mean square error (RMSE) or mean absolute error (MAE)) or a confusion matrix to compare the four models. RMSE would be for the OS models, and a confusion matrix would be for the Death models.

After picking random forest, regression, gradient boosting, or parametric survival regression, you can then optimize that model.

For information on looking at interaction effects between variables, see the previous post below:

A first trial...

I'm not sure about online tutorials, but the book "An Introduction to Statistical Learning" by James et al. should tell you everything you need to know. It has an entire chapter dedicated to survival analysis.