已知椭圆C:$\frac{x^2}{a^2}$+$\frac{y^2}{b^2}$=1与双曲线$\frac{x^2}{4-y}+\frac{y^2}{1-y}=1\left(1<y<4\right)$有公共焦点，过椭圆C的右顶点B任意作直线l，设直线l交抛物线y²=2x于P、Q两点，且OP⊥OQ．

（Ⅰ）求椭圆C的方程；

（Ⅱ）在椭圆C上，是否存在点R（m，n）使得直线l：mx+ny=1与圆O：x²+y²=1相交于不同的两点M、N，且△OMN的面积最大？若存在，求出点R的坐标及对应的△OMN的面积；若不存在，请说明理由．

    Peter plays basketball for the kids basketball club. He usually gets up at 5:30 and runs in his school from 5:40 to 6:40.After running, he has breakfast at 7 o'clock. For breakfast, he eats some eggs and vegetables. At 8:00,he plays basketball with his friends. They play for a long time. At about 12:00,they have lunch. For lunch, Peter has lots of vegetables, chicken and fruit. At 3 o'clock in the afternoon, Peter goes to the kids basketball club. Peter has dinner at about 7:00 in the evening. After dinner, he watches basketball games on TV. Peter usually goes to bed at 9:30.

因为父母残疾，自强的陈容从7岁起就承担起了大部分家务，成为父母的小小顶梁柱。她被评为重庆市首届“五心四好”美德少年。陈容的自强事迹告诉我们（   ）

①自强是一个人活出尊严、活出个性、实现人生价值的必备品质     ②自强是我们健康成长、努力学习、将来成就事业的强大动力

③自强是一种精神，一种美好的道德品质                                             ④要做一个自立自强的人