了 is a particle with no actual meanings, but there are three kinds of particles: 状态助词, 语气助词 and 结构助词. 了 is both a 状态助词 and a 语气助词.
When it is used as a 状态助词, it shows the thing the speaker talks about is finished or started but have not ended, and should be after the verb or verb phrase; when it is used as a 语气助词, it is just a sign of statement and must be ...
This dictionary definition addresses the use of 了:
E.g. 小王来信了 / 都四月份了，天还这么冷 / 天快亮了 / 要是不走就见到他了。
Basically, it says this use of 了 is placed at the end of a sentence, introducing a new circumstance or change. The new circumstance can be something already happened, or will happen, or a hypothesis.
了 means 'at present'
So 找到你了 means, as present, I have found you and 我想家了 means, at present, I miss home. When you add 了 after the verb the meaning changes 我去找到了你 means I went to find you, and 我想了家 means I thought about home.
Interestingly you can also say 我找到你啦 where 啦 sounds like 了 but 啦 indicates exclamation. An example is 她们赢啦！ （they won!）Another example ...
我找到你 - "I find you". This sentence lacks clarity on whether the act (find) has happened in the past, now, or is ongoing.
我找到你了 - "I find you now" or "I found you". These two indicate the act is either completed now (the former) or was completed in the past (the latter).
我最喜欢看篮球比赛 = 我最喜欢看篮球比赛了 - As this sentence is a general ...
Your translation is precise.
In my opinion, 了 here emphasises that the affair 职务没了 HAS occurred. Consider the following variation.
I would say that's also OK.
This is also good. “没有职务了” sounds like a speech from 王建男, so I prefer to use a 破折号（——）.
Last but not least, I agree with Romanazzi that 了 can ...
As @dan said in the comment, here 没 is not the negation of 了, but of the verb 有.
we don't use 了 in conjunction with 没
That is true (with only a few exceptions) if the structure of the sentence is 没(有)+Verb. But in our case, 有 is the verb and the structure is Verb+Noun.
In Cantonese, a normal positive question takes the form of "P non-P", which covers all the values of the domain P. For example:
咪(mai6) is a contracted form of 唔係係. It also covers the whole domain P, but it takes the form of "non-P P". It is akin to a negative question, which usually indicates a kind of surprise or doubt. ...
(v) don't; shouldn't; mustn't
咪行住 (don't go yet)
咪郁 (don't move)
咪使旨意 (don't count on it)
Notice: It is read as /mai5/
(1) isn't; wasn't; aren't (used as a syllable blending from m4hai6 唔係)
(2) (often used with 囉) then; as a result; might just as well
冇麵包咪食蛋糕囉 = If there's no bread, (then/ might just as ...