You are a great mommy! I know some people who do time-outs, but I agree with you--I just don't see how a little toddler could understand that. My daughter is 21 months and there's no way she would comprehend a time out. What I have done:
1) Distraction--offer her something she CAN do instead
2) Natural consequences--if she throws a toy or dumps out the Cheerios, she has to pick up... of course she won't want to, so I guide her--that is, move her body towards the toy or hold her in place next to the toy/Cheerios until she complies...she can't leave until she does it
3) Explain why--when she hits me or pulls my hair in jest/to be funny, I ask her to stop and briefly explain that it hurts. When she has to put the pacifier/lovey in bed but doesn't want to, I help her put it away and explain that it stays there so it will be there at bedtime tonight.
4) Tandem time-out--I remove her from the source of aggravation/go into a different room, get face to face at eye level with her, and explain the problem and an acceptable alternative (for example, when she is screaming b/c the other kid won't give up a toy I would say "taking the toy out of someone else's hands is not okay, you have to wait till he is done with it or play with something else"). It is different from being isolated in a corner or naughty chair because you/parent are with her--the point is to deescalate the raw emotion AND teach good behavior. Making her sit alone will not teach her because she does not yet have the cognitive ability to reflect on her actions and think logically about it.
As for the "nooo miiine" I'd bet that she's just practicing pronouncing and expressing herself. Based on the context I agree with you that she doesn't know what it means. When she throws those tantrums, be strong and don't give in--make her calm down before you agree to her she wants IF it is reasonable to you, and just say "no, no, no..." if it is not reasonable. She will learn that you mean what you say if you don't give in and say yes after saying no.
You seem to understand your daughter's needs so keep up the good work mommy!