‘Resolve’ has the implication that the issue has been difficult, and that you have been thinking about it for some time. All of the examples you give could use this word, which implies something more serious than simply to decide. Whether you say ‘decide’ or ‘resolve’ will depend on the context of the statement : if you have explained the issues involved in reaching the decision, and how difficult it has been, ‘resolve’ will be appropriate.

решить Sometimes it is interchangeable, but 'to decide' is more common. To resolve to do something, involves a strong will, a firm decision, and it also has the meaning of 'to solve', i.e. I resolved the puzzle, I resolved the issues between the co-workers. Resolve can be used for problems (maths problems, relationship problems) as meaning 'to find a solution'. 'To resolve' and 'resolution' indicate a very strong commitment to the goal, a firm decision, involving willpower. In most other cases, 'to decide' is much more common.

Yes. But Resolve is a much stronger word. It can carry more weight than decide, although they essentially mean the same thing.

Decided should only be used in all cases of the examples provided

In context |obsolete| lang=en terms the difference between resolve and decide is that resolve is (obsolete) to relax; to lay at ease while decide is (obsolete) to cut off; to separate. As verbs the difference between resolve and decide is that resolve is to find a solution to (a problem) while decide is to resolve (a contest, problem, dispute, etc); to choose, determine, or settle. As a noun resolve is determination, will power.