Please, check if my explanations of the phrase is right
To face up to something - dealing with problem things or people.
It’s often mispronounced – the word or phrase said wrong.
Don’t take hasty decision – fast decision that probably is wrong.
Make sure – to check if decision is right.
In the long run/term – successful idea that will be good all in all
Keep in mind – to save any idea in your head.
Work out something – to create a new strategy (or material thing?)
Be obsessed – to have a great interest doing smth or to be crazy about something.
Customers/clients – people who want to purchase something from sellers.

Question

Please, check if my explanations of the phrase is right
To face up to something - dealing with problem things or people.
It’s often mispronounced – the word or phrase said wrong.
Don’t take hasty decision – fast decision that probably is wrong.
Make sure – to check if decision is right.
In the long run/term – successful idea that will be good all in all
Keep in mind – to save any idea in your head. 
Work out something – to create a new strategy (or material thing?)
Be obsessed – to have a great interest doing smth or to be crazy about something.
Customers/clients – people who want to purchase something from sellers.

Answer

To face up to something - to choose to deal with something (implies it is difficult or unpleasant)
Don’t take a hasty decision – Don't rush a decision. Take your time before deciding.
In the long run/term – long term / medium term / short term. These are shorter or longer periods of time. It will depend on what it is referring to. e.g. his stock investments fell this week, but in the long term they will recover.
Keep in mind – to continue thinking about something
Work out something – to solve a problem
Be obsessed – to have a great interest doing smth or to be crazy about something. yes, and it also implies that it's in a negative way. e.g. 'he was obsessed with his ex girlfriend and couldn't leave her alone.'
Customers/clients – people who receive or consume a product or service for whatever reason.

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also 'work something out', not the other way around.

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thanks a lot

Answer

"long-term" (как прилагательное) = долгосрочный; "in the long run" = в конечном итоге, в долгосрочном перспективе. Не обязательно означает, что будет какой-то успех.  "Keep in mind" = (следует) иметь в виду

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Thank you, now I know that American option is "make a decision" instead of "take a decision".