Answer 1

Math you should know (use Khan Academy):
-Linear Algebra
-Statistics

Math you should know if you actually want to be a very good data scientist:
-Linear Algebra
-Statistics and Probability
-Discrete Math (if you want to understand algorithms. Usually a pre-requesite before taking any algorithm course. MIT Open Coursework is very helpful)
-Differential Equations (essentially what a model is)
-Multivariate Calculus (partial derivatives, among other things)

Use Khan Academy for everything listed above except for Discrete Math.

You need a very strong understanding of Probability, specifically Bayesian. That should be included in my other links.

The tools Alket listed below are good. Use those for the practice link I have listed below.

As for the actual algorithms, Andrew Ng's open course is recommended. Page on coursera.org. 

Take all the classes listed on the data science coursework at Udacity if you are starting with no knowledge whatsoever. Course catalog - Udacity.

If you need practice, use The Home of Data Science.

https://www.google.com/amp/s/www.quora.com/What-are-the-basic-machine-learning-tools-required-for-data-analysis-Where-can-I-learn-about-those/amp