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Can I say,

(a) She promised she will look after the plant for a long time.

(b) She hoped the plants will grow healthily.

(c) She hoped (that) the plant will grow into a big and beautiful rose plant.
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Strictly speaking, you must use 'would' in such cases (sequence of tenses rule). But in spoken speech you sometimes can say 'will', neglecting the rule. For example, when she promised it just a second ago and you confirms that she did it. But 'will' after 'hoped' sounds wrong to me in any case.
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She promised she will would look after the plant for a long time.
OR She promised she will to look after the plant for a long time.

She hoped the plants will would grow healthily (well).

Health is associated mostly with human beings or animals, less often with plants.

She hoped (that) the plant it will would grow into a big and beautiful rose plant
OR She hoped (that) the plant will would grow into a big and beautiful rose [plant / bush / tree].

It's awkward to repeat the word plant.

CJ
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Comments  
(b) She hoped the plants will grow healthily / healthy.

Is there correct? which is better? why?
Are they same in meaning? healthily / healthy? are they correct?
Students: Are you brave enough to let our tutors analyse your pronunciation?
 CalifJim's reply was promoted to an answer.