How do you know that the assumptions of the model have been satisfied, and it’s ok to run the algorithm? when using any simple algorithm like logistic regression, svm or even complex ones, how could you know that it’s ok to run the algorithm and use it in the industry?
for example :when using logistic regression i assume that the data is represented by a specific function, how could i know that my assumption is good?
 A: It's a matter of thinking about the problem and deciding whether the model could provide a reasonably good approximation to the outcomes. As noted by Bernhard, it will (in almost all situations) only ever be an approximation, but it might be a good one - or at least one that is good enough to be useful. E.g. when we have a success/failure outcome and very few failures, linear regression will often been a very poor choice, while logistic regression could be appropriate. If we realize that data comes in batches (e.g. different production runs), we then consider whether we should take that into account in our model. 
Additionally, we of course look at how well our model performs - e.g. when we see that a linear regression model frequently predicts negative proabilities (or a negative number of failures), we would hopefully realise that it's a bad model, even if this had not occured to us on theoretical grounds before.
If we realise that we know a lot of the underlying process through which the data arises, we may try a more complex model to reflect this knowledge. E.g. the successes and failures are actually arising from something being subjected to some stress or exposed to some risk for some period of time and the longer the time is, the higher the probability of a failure, then a time-to-event model may be a better choice than logistic regression. On the other hand, if the times are risk do not vary too much (and perhaps we do not even know them), then logistic regression may or may not still provide a good approximation, depending on what we want to do. E.g. if we want to change something about the underlying process (such as changing the time at risk in order to reduce failures to a certain level), more complex modeling that takes into account the aspects we wish to vary is needed, otherwise we cannot really say much about how we should change the process.
A: That one is easy to answer: in almost any case you can rely on the assumption, that your assumptions are wrong. Everything that says "normally" distributed is wrong, as nothing in reality spans form minus infinity to plus infinity. All you can say is: My prediction is only as good as my assumptions are: Models are a simplified picture of the "true world" and no modell explains everything. Just don't rely on the results of any prediction more than the usually large number of assupmtions in any modell reflect the truth. 
Can you cross the road, when there is a green light? Most of the time yes and green light will be one ooof the best predictors when to cross the road safely. However if there is a fest somewhere around and people drink and drive, you should be more carefull than if not. Even if the green light is on.
Using a certain method is not a question of yes/no but on how much you will rely on the result.
