Do auxiliary verbs always serve to express a mood or aspect that is different from simple indicative (or a tense)? Or are there cases where a sentence is in simple-indicative-present with the presence of an auxiliary verb?
No, the use of auxiliaries is not directly linked to aspect, mood or tense in the first place. This may be so in some or many cases by coincidence when morphological or syntactic marking is not available, but the link between auxiliary verbs and TAM is not a logical necessity.
On the one hand, there are (even in English) cases where the use of auxiliaries does not change aspect/mood/tense:
- They charged him --> He WAS charged (change to passive voice, but not indicative or tense)
- You realize --> You DOn't realize (negation, same tense and mood)
- He responds --> DOES he respond? (qustion formation, grammatical change but not about mood, tense or aspect)
- I think --> I DO think (enforcement, no kind of grammatical change)
On the other hand, there are numerous cases where TAM is expressed other than by an auxiliary verb:
- I play --> I playED (morphological marking of tense)
- You wash the dishes --> Wash the dishes (imperative mood by syntactic marking)
- French: Tu pars --> Je veux que tu PARTES (subjunctive mood)
- langauges with evidentiality, apectual, ... affixes
And there are even cases where an auxiliary is used for indicative present, namely present progressive (if you take this as the "normal" present) in English:
- Mary IS cooking
So the answer is no, auxiliaries do not always express TAM differing from "simple indicative present", not even necessarily grammatical features.
No, auxiliary verbs don't always express something other than simple indicative. Yes, there are cases where a sentence with an auxiliary verb is in the simple indicative. For instance, "Hal is a fisherman." The "is" is an auxiliary verb, since it inverts with the subject in the corresponding yes-no question "Is Hal a fisherman?", and it is a simple indicative.
No, e.g. in Czech, the past tense is expressed by the copula verb "být" (to be) and the past participle of the main verb. It is the main verb that expresses the aspect (perfective/imperfective).
Dělal jsem - I did / I was doing (imperfective aspect)
Udělal jsem - I did / I have done (perfective aspect)
On the other hand, the mood is expressed on the auxiliary
Dělal jsem - I did
Býval bych dělal - I would have done
So this is language dependent and structure dependent.
E.g. in Czech it is currently impossible for the verb "být" to take over the aspectual function in the past tense as this is one of the few verbs that do not distinguish perfective/imperfective aspects. On the other hand in the future tense, the imperfective verbs form future with synthetic future tense of "být" + infinitive of the main verb, while for perfective verbs, the future is expressed merely by their "morphological present", since there is nothing like perfective present tense:
Dělám - I do / I am doing (imperfective aspect, present tense)
Udělám - I will do / I am going to do (perfective aspect, future tense expressed by "morphological present")
Budu dělat - I will do / I will be doing (imperfective aspect, future tense)
So here, the aspect is kind of expressed by the presence of the auxiliary (if not on the auxiliary, again the copula verb does not distinguish the aspect) - this can be seen with verbs that normally do not distinguish aspect (typically verbs of latin origin)
Informuji - I inform / I am informing (imperfective, present)
Informuji - I will inform (perfective, future - expressed by "morphological present)
Budu informovat - I will inform / I will be informing (imperfective, future)
In Portuguese, there are at least two different kinds of auxiliary verbs.
First, there are syntactical auxiliaries, that change grammatical features of the main verb. Those are ir (to go), ser (to be), estar (to be, too, but the meaning is quite different from "ser"), ter (to have), and haver (to have, but in different contexts - and, no, it is not a cognate of "have"; their similarity is a mere coincidence).
Ser is used for changing voice, not tense or aspect:
Joana processou José. - Jane sued Joseph.
José foi processado por Joana. - Joseph was sued by Jane. (foi is the past simple of ser.)
The others are used for tense/aspect modification. Ir + infinitive of the main verb indicates future or conditional, estar + gerundive of the main verb expresses "imperfect" (or continuous) aspect, ter and haver + past participle of the main verb express perfect aspect:
Eu vou dormir. - I am going to sleep. (Vou is the indicative present of ir.)
Eu ia dormir. - I was going to sleep.
Eu estou brincando. - I am joking.
Eu havia dormido. - I had slept.
Eu tenho dormido. - I have been sleeping.
Those verbs can also be used as main verbs on their own, with perhaps the exception of haver, whose present indicative, há, seems to be evolving into some kind of particle - to the point that there is generalised confusion with the homophone preposition a.
Second, there are "modal" auxiliaries that change the semantics of sentences, such as querer (to want), poder (can), precisar (to need), parecer (to seem), without messing with tense or aspect (unless they are themselves flexed for tense/aspect).