5He will have to get up early to go to school.
He will go to school tomorrow.
Is "will" a modal auxiliary verb or just a helping verb in the sentences above ?
WILL is a modal (auxilary) verb in those sentences.
or is "will" always considered a modal auxiliary verb ?
There are lexical (i.e., non-modal) verbs: will - definition. American English definition of will by Macmillan Dictionary
have + to = should they be analysed together as a semi-modal auxiliary or should they be considered separately, i.e.,
have = primary auxiliary verb
to = preposition or something else ?
Most writers on grammar consider 'have to' to be a semi/quasi- modal (auxiliary).
Do we recognise a modal verb by the fact that it does not take any inflections ?
The core modals do not take inflections, do not use DO in negative and interrogative forms, are followed by a bare infinitive, etc.
In that case "will" would be a modal but not "have to" ??
Student or Learner