Are inflectional morphemes always suffixes?
In english? yes*
* this depends on your analysis. Some people might consider
ablaut as a kind of inflectional morpheme.
s
ing->s
ang->s
ung
m
an-> m
en
m
ouse-> m
ice
Generally it's regarded as a sound change (look up
Apophony and related pages on wiki), so I would stick to that for the purposes of EngLang. But if you're bored one day, the question "Is ablaut inflection?" might provoke some discussion in class.
E.g. determine --> predetermine is a derivational morpheme?
determine --> determines is an inflectional morpheme?
You're spot on with those examples of derivational morphemes vs. inflectional morphemes. Why not make yourself some lists? List all the inflexional morphemes you can think of, then as many derivational morphemes are you can. What test could you apply to a morpheme to provide evidence of it belonging to one category or the other? does the morpheme affect the syntax or agreement with verbs/nouns?
As for contractions and elisions, i'd've said you'd wanna have a cuppa 'n look 'em up on the 'net.