Could you please explain the difference in meaning between 設計｛せっけい｝ and 提案｛ていあん｝? Could they be interchangeable to mean "to suggest"? Thank you in advance.
提案 is to suggest in the sense of to make a proposal. You always need another person (for example your business client) to do 提案. In another word, 提案 refers to saying "Let's do ～". Note that 提案 never means to suggest in the sense of to imply/say/remind (as in "The lion suggests bravery" or "The letter suggests he's angry").
設計 is to design (a product, a building, software, etc.) or to engineer. As long as you have a good engineering skill, you can finish 設計 all by yourself with a pen and paper, or CAD software. I don't know when this means to suggest. 設計 always refers to engineering design which does not require a sense of beauty. Graphic design, interior design, dress design and such are usually called デザイン.