How things become easier when we do things continuously / repeatedly? What are habits, and why do they stick? Lord Buddha said that we even bring habits into next lives. Why does that happen? How come it is powerful enough to continue from life to life?

There are some variations of habits. Some needs mental effort (like studying, or meditating etc.), some needs physical effort (exercising etc.), and some doesn't need any effort, meaning that every day actions (eating, playing etc.). (By effort i mean the energy needed to do something, and habits requires less actual effort to do something).

I have the general idea about how habits works. We may be able to find shortcuts, and get new ideas when we do things repeatedly. But, it is hard to understand the way our habits vary. Can anyone give me a clear / deep explanation about habits?

Or are habits conditioned by impermanence, cause and effect or karma that I should accept as the nature of existence/the world? If it is, please post the name of respective sutta where Lord Buddha talked about habits, so I will be able to believe it without doubts.

Kind regards.
Maybe your looking at it the wrong way. I am not sure of an exact sutta or even any sutta that says this exactly but habits passed onto another life can be because of the karma accumulated. 

For example let take the following scenario.
If your a physical trainer, you would most likely train all your life to be physically fit. Now as a trainer, you get other people (your clients) into physical training hence you do the "dana" or "giving" of physical training to lots of people. Since you have that karma of "giving out physical training", your most likely to get "physical training" as a reward in your next life. Hence there is a high chance in your next life you will be really into physical training. While you do this, you will also inspire someone else to be a physical trainer. Again giving the "inspiration to be a physical trainer". Next life, someone will inspire you to be the same as a result of your karma.

If you inspire someone, you will be inspired by someone. You make someone do something, someone else will do the same back to you. This is the karmic law. Obviously its not this simple but in a bird's eye view, roughly this is probably the cause of a habit being born on a person and then continuing until that habit is dead.

Karma is subjected to impermanence like everything else. Hence eventually it will fade away. So you won't have a forever samsara habit.