It's highly recommended that every time you learn a new verb, you learn it together with its possible reflexive pronouns (se, si), prepositions and cases.
The problem is, of course, that many verbs have more than one valence, for example "čekat +ACC" (await/expect someone) and "čekat na +ACC" (wait for someone), or "vážit +ACC" (weigh something) and "vážit si +GEN" (respect something/someone), and you might only be exposed to one of them when first encountering the verb.
Good question. It's a little more complicated:
The stressed positions can only be filled with the longer pronouns (mně, tebe, tobě, jeho, jemu...)
In the unstressed 2nd position, the short pronouns (mi, tě, ti, ho, mu) are preferred, but the longer ones are not incorrect. Using the longer pronoun in the unstressed position is almost equivalent to moving it to a stressed position, i.e.:
- Proč ti dala svoji sukni? -- Why did she give you her skirt?
- Proč tobě dala svoji sukni? -- Why did she give you her skirt? (amazement at you)
- Proč dala svoji sukni tobě? -- Why was it you (and not someone else) that she gave her skirt to?
That said, "mně/mi" is still special, because some speakers just use "mně" (dative) in all positions even if they don't mean to stress it. In writing, it's bad style. In speech, it's a minority of speakers and honestly, my ears don't like it. I think it happens more commonly in Moravia than in Bohemia. I would personally only write "Proč mi dala svoji sukni?" and if I spoke it with "mně" in that position, I would clearly emphasize "mně" with my voice.
I would just suggest we avoid making it look as if even the spoken unstressed "mně" were somehow undesirable. I get that it does not please your set of ears, but I heard it and said it myself much of my Czech life. One could try arguing that hearing it does not mean it is standard even in spoken language, but we have ÚJČ for that, and
Kratší tvar 3. pádu (mi) se užívá jen příklonně, delšího tvaru (mně) se však užívá jak v pozici po předložce a při důrazu, tak i v pozici příklonné.
even fails to discourage the form in writing and formal speech. (No, I am not arguing for its use in those settings.)
Our users are likely to hear the unstressed "mně" in the wild if they get there, so the practical approach would be to expose them to it, lest they mistakenly consider each unstressed dative "mně" the accusative "mě".
How the exposure to the various clitic and stressed pronoun forms should be staged is a worthy subject for elsewhere.
Yes right, it's my personal pet-peeve, let's say. It has always puzzled me why some people use "mně" in place of "mi" to the point of wondering (when I was young) whether they actually use the wrong case ("mě"). And I mostly heard it when I visited the Moravian side of my family where it was used alongside a wide range of other dialectal words+grammar (Moravian Slovakia, so quite a thick dialect, especially a few decades ago). Then I was even more puzzled when I occasionally heard it even in Bohemia.
And even though ÚJČ allows it, it's really not that common. For instance, googling "dej mi" gives 888K results. Googling "dej mně" gives 12K results where a lot of them are grammar discussions or texts concerning a dialect or dated texts ("Dej mně, Bože...")
But yes, it's not wrong. Using it is a matter of personal taste (and dialect). I'm not saying it shouldn't be in the course.