You are right that 'fire' is a less formal version of 'dismiss', and both are very negative. The employee usually must have done something bad. Remove and discharge are rarely synonyms though. Discharge only applies to military jobs, and is not necessarily negative. 'remove' might be used for elected representatives, but would involve a very different process. 'Lay off' is not temporary - but is usually used when a group of people are all laid off at once. It is usually because the company needs to save money. 'Made redundant' is another synonym for that. And yes, retiring is when an employee decides to stop working because of their age. BUT - depending on the country, different rules can apply, and these words can have slightly different meanings.

What word is used if employee (not employer) want to stop working and dismiss?

Here are some more verbs, all of which mean "dismiss (an employee)." They are colloquial. ---- sack; boot; bounce; can. /// All of these verbs have other meanings as well, so you must rely on context. In addition, "to pink slip" also means "to dismiss."