The family permit is borderline topical, it has a limited duration and people do use them facilitate travel. On the other hand the permit is often a prelude to taking up residence, hence borderline.
Your husband is an EEA national (assuming not British) and you are filling out an EEA family permit application to join him in the UK. The EEA family permit runs for 6 months after which you must upgrade to a residence permit. So your answers on the application are preliminary, and their analysis window is limited to 6 months, not further.
On which date will you leave the UK? what should i answer? once it is
asked the day month and year.
You can take the expiry date of your passport and subtract two months and use that date to answer the question.
How long do you intend to stay in the UK?
Calculate the interval between now and the date you calculated in the first step. Use that interval to answer the question.
Do you intend to work in the UK? if yes provide details I intend to
work, and what details should i provide?
Answer yes. The details are that you and your husband will seek employment for you once you get settled in. If you have a great skill, like brain surgery, you can put that down also.
Be sure to include your insurance and evidence that your husband is exercising treaty rights.
In 6 months your next step will be getting a residence permit. Questions about the EEA residence permit should be posed on the Expats site, which is here https://expatriates.stackexchange.com/questions