- What is certain is that apprentice and company is not a contract of employment...
的 functions as the second 'is' above, such that one can omit the object "fact" "What is certain is (the fact that) apprentice and company is not a contract of employment...". This sentence is a bit colloquial and hence the grammar here may appear strange.
- (About) this company I enetered in September, my boss said the first few months are for training.
EDIT: The first 的 emphasis "This company" is the subject or topic of discussion, and "Entered in September" is merely a descriptor or adjective-phrase (的 has the ability to convert most clauses/words before it to adjective). 的 also serves as a rhythm of speech particle so that if omitted it won't sound natural, unless you replace it with “了”,i.e. “我九月份进了这家公司”. This results in a sentence that instead of emphasizing the company is in question, I is put as the subject and the time (September) is emphasized as the important information. As in "I enetered this company in September (I am the subject topic, and the important thing is the time I enetered this comapany). Further to OP's post, OP asked what if one writes "我是九月份进的这家公司", this put even more emphases on the fact that "I started in September" as important information.
The second 的 shortens the more correct but cumbersome sentence structure:
"前面几个月是实习期的几个月". Again this is a bit colloquial and it is not uncommon for the grammar to seem a little bit informal.
I would personally however said "老板说前面几个月是实习期", which is more compact and grammatically sound.