First of all we have to make a distinction between auxiliary verbs (do, be, have) which are used to form the tenses of ordinary verbs, and modal auxiliary verbs, which are auxiliary verbs but also convey modal meaning (possibility, probability, future, condition, etc).
AUXILIARY VERBS
BE
IMPERSONAL:
EMPTY SUBJECT
NATURAL PHENOMENA
TIME AND DATE
DISTANCE
CLEFT SENTENCES
AUXILIARY
CONTINUOUS
PASSIVE
BE GOING TO
BE ABOUT TO, BE TO
BE TO INFINITIVE: obligation, certain future,
LINKING VERB
FULL VERB: EXIST HAVE
AUXILIARY VERB: PERFECT TENSES HAVE TO CAUSATIVE HAVE POSSESSION TAKE, CELEBRATE, EXPERIENCE, EAT, DRINK, ENCOUNTER (TROUBLES) DO AUXILIARY IMPERATIVE AVOID REPETITION OF THE PREVIOUS VERB
ADDITIONS TO REMARKS and so do I QUESTIONS TAGS: don´t you?
SHORT ANSwERS: yes he did DO + ING do the shopping FULL VERB DO / MAKE:
When we don´t say exactly what activity is done: what are you doing
Make implies the idea of construction: make a cake, a castle of sand, a kite, a carving…
In other cases there are no general rules:
Do harm, good, business, a favour, homework
Make an offer, a suggestion, a decision, an effort, an excuse, a mistake, a noise, a phone call, the best of, love, war, a bed!
MODALS SEMIMODALS