I think you've got a bit confused here. First of all
a) You need to distinguish between word stress and sentence stress - which are two different things. See this thread
for another relevant discussion.
b) Primary and secondary stress applies only to word stress - so if a lexical item is one syllable only, it has - as you say - primary stress (marked '), eg road /'rəʊd/. But a longer word will have one syllable with primary stress and others which are either unstressed - eg the second syllable in swimming
/'swɪmɪŋ/ or have secondary stress (marked ,)- so eg in necessary
the first syllable has primary stress, the third secondary stress and the second and fourth are unstressed : /'nese,seriː/
c) English is a stressed timed language. this means that the time it takes to say an utterance is (roughly) dependent on the number of stressed syllables it contains - not on the total number of syllables. To achieve this, the unstressed syllables get "squashed up" or "reduced" in between the stressed syllables. This is true for unstressed syllables in lexical items, but also for unstressed grammatical items (pronouns, prepositions, auxiliaries, articles etc.) This reduction happens done in a number of ways - think eg of the omission of sounds that you get in contractions - /ɪts/ rather than /ɪt ɪz/. But another way is vowel reduction.
d) Vowel reduction means that the vowels in the unstressed syllables, tend to be replaced by a similar but shorter vowel - often but not always the schwa. Look at my transcription of necessary
above. That's how it might be pronounced if spoken in isolation, clearly and slowly. But in connected speech it would be more likely to be pronounced as /'nesə,serɪ / or / 'nesə,srɪ / Notice the changes to the vowels in the unstressed syllables. And in fact in the second version the vowel in the original third syllable has disappeared, so it's now a three syllable word with the pattern first syllable = primary stress, second syllable = unstressed and third syllable = secondary stress.
So basically, a likely connected speech transcription of your sentences (which i've adapted a bit to make things clearer) would be as follows:
(a) I think she was in the city yesterday
/ˌʌ 'θɪŋk ʃɪ wəz ɪn šə ˈsɪtɪ 'jestə,deɪ/
(b) March is usually a beautiful month
/'mɑtʃ ɪz 'juːʒlɪ ə ˈbjuːtəfəl 'mʌnθ/
One syllable lexical items must by definition have primary stress - so will never change. Lexical items with more than one syllable will always have primary stress on the same syllable, but the other syllables may be reduced in some way - eg by omission of a sound or vowel weakening. But that vowel weakening, whether on lexical items or grammatical items, isn't always to the schwa - as you can see above where /aɪ/ is weakened to /ʌ/ and /iː weakens to /ɪ/.
e) On top of all that there's intonation and the placement of the tonic - ie the syllable which carries pitch change as well as stress. But that was dealt with in the thread I linked to above, so have a look there.