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The problem is that there is no one-to-one correspondence between the English word "would" and a single Chinese word. Each sentence must be translated according to the original meaning in English.
Your first sentence is basically a polite way to say you want to do something. Instead of saying, "I want to visit you this weekend," you're expressing respect by saying it more politely, with "I would like to visit you this weekend."
In this case, an expression in Chinese that reflects this polite version of *your* desire to do something would be to ask for permission, or to use a verb that expresses respect in Chinese such as: 這週末我想／希望拜訪你，不知你方不方便。Note that 拜訪 is a polite way to say "visit someone" in Chinese.
Your second sentence expresses a polite request for someone to do something for you. In this case, to express this polite request of another, you can use a verb such as please, or "may I trouble you with," such as 請／麻煩你幫我轉寄我們上一封電子郵件。
When the English word "would" is not used an expression for politeness but as a condition or alternative, such as "I would have studied harder if I had known the test was going to be this hard," then you simply use the present tense in Chinese: 我如果早知道這考試會這麼難，我會更加用功。
