Is investing $4,000 in clothing trade, with the condition of a fixed monthly profit of $80, and the inability to retrieve the capital before one year, considered impermissible (haram)?

You must repent for any shortcomings in seeking knowledge. A Mudarabah (profit-sharing) contract in which one of the partners has a known, non-communal share of the profit is invalid and must be annulled. The Mudarib (investing partner) is entitled to a reasonable wage (ujrat al-mithl) or a reasonable share (hissat al-mithl), and you must advise him of this.

The contract is permissible, and either partner has the right to dissolve it. If the Mudarib refuses to return the capital or correct the contract, he is considered a usurper. It is permissible to take whatever money he provides for expenses until the capital is fully recovered. The owner of the capital is entitled to the profits generated from her money after the Mudarib's reasonable wage for the period before the demand for annulment. After that, he becomes a usurper.

Scholars have differed regarding the profit from usurped money. Sheikh Al-Islam Ibn Taymiyyah favored the view that the profit should be divided between the two parties, similar to a Mudarabah. Therefore, whatever profit you are certain is your share, it is permissible for you to take it and count it towards what has been received. What you are not certain of, you are not entitled to take.