The contract has a large number of illegal conditions in it.I would simply walk away.
Legally you should get 10 paid days,
Article 60 (Annual Paid Leave) (1) An employer shall grant 15 days' paid leave to a worker who has registered not less than 80 percent of attendance during one year. <Amended by Act No. 11270, Feb. 1, 2012> (2) An employer shall grant one day's paid leave per month to a worker who has worked consecutively for less than one year or registered less than 80 percent of attendance during one year, if the worker has offered work without an absence throughout a month. <Amended by Act No. 11270, Feb. 1, 2012> (3) If an employer grants a worker paid leave for the first one year of his/her service, the number of leave days shall be 15 including the leave prescribed in paragraph (2), and if the worker has already used the leave prescribed in paragraph (2), the number of used leave days shall be deducted from the 15 days of leave. (4) After the first year of service, an employer shall grant one day's paid leave for each two years of consecutive service in addition to the leave prescribed in paragraph (1) to a worker who has worked consecutively for 3 years or more. In such cases, the total number of leave days including the additional leave shall not exceed 25. (5) An employer shall grant paid leave pursuant to paragraphs (1) through (4) upon request of a worker, and shall pay ordinary wages or average wages prescribed in employment rules or other regulations during the period of leave. However, the leave period concerned may be changed, in cases where granting the leave as requested by the worker might cause a serious impediment to the operation of the business. (6) In applying paragraphs (1) through (3), a period falling under any of the following subparagraphs shall be considered a period of attendance: <Amended by Act No. 11270, Feb. 1, 2012> 1. A period during which a worker is unable to work due to occupational injuries or diseases; 2. A period during which a pregnant woman does not work on leave taken pursuant to the provisions of paragraphs (1) through (3) of Article 74. (7) The leave referred to in paragraphs (1) through (4) shall be forfeited if not used within one year. However, this shall not apply in cases where the worker concerned has been prevented from using the leave due to any cause attributable to the employer.Article 61 (Promoting the Use of Annual Paid Leave) If a worker's leave has been forfeited for non-use pursuant to Article 60 (7) despite the fact that the employer has taken measures described in any of the following subparagraphs to promote the use of paid leave prescribed in Article 60 (1), (3) and (4), the employer shall has no obligation to compensate the worker for the unused leave, and shall not be deemed to have caused the non-use attributable to the employer's action under the proviso of Article 60 (7): <Amended by Act No. 11270, Feb. 1, 2012> 1. Within the first 10 days of the six months before unused leave is to be forfeited pursuant to the main sentence of Article 60 (7), the employer shall notify each worker of the number of his/her unused leave days and urge them in writing to decide when they would use the leave and to inform the employer of the decided leave period; 2. If a worker, despite the urging prescribed in subparagraph (1), has failed to decide when he/she would use whole or part of the unused leave and to inform the employer of the decided leave period within 10 days after they were urged, the employer shall decide when the worker uses the unused leave and notify the worker of the decided leave period in writing no later than 2 months before the unused leave is to be forfeited pursuant to Article 60 (7).Article 63 (Exceptions to Application)The provisions of this Chapter and Chapter V as to working hours, recess, and holidays shall not be applicable to workers who are engaged in any work described in the following subparagraphs: <Amended by Act No. 10339, Jun. 4, 2010> 1. Cultivation of arable land, reclamation work, seeding and planting, gathering or picking-up or other agricultural and forestry work; 2. Livestock breeding, catch of marine animals and plants, cultivation of marine products or other cattle-breeding, sericulture and fishery business; 3. Surveillance or intermittent work, for which the employer has obtained the approval of the Minister of Employment and Labor; 4. Any other work prescribed by the Presidential Decree.