1. Describe concisely the possibilities for adverb placement allowed by this grammar tool. Are any of the allowed strings ungrammatical in English?
Adverbs can be left adjoined to either V' or I'. No right adjunction of adverbs is permitted by the tool. The adverbs always and carefully adjoin freely to both V' and I' but completely adjoins only to a V' whose head is a main verb (FINISH) but not when the head of V' is an auxiliary (HAVE). More than one adverb can adjoin above the same head, yielding sentences like:
But since the adverb order is free, the following ungrammatical string is also generated:
*John has completely always finished the work.
When an adverb is adjoined to the V' of the main verb and that verb moves (using G1) the resultant string is also ungrammatical:
*John finished always the work.
2. How do grammar options G1, G2, and G3 differ? G1 allows raising of both the main verb and the auxiliary; G2 allows only lowering of tense onto both the main verb and the auxiliary; G3 allows only raising of the auxiliary verb and lowering of tense onto the main verb. With the free word will in I, no raising or lowering is allowed.
3. Looking only at the variant forms generated by this grammar, is there evidence that English sometimes exhibits verb-movement to I?
There is no such evidence. Evidence of V-to-I movement based on adverb placement (as opposed to negation or question formation) appears when an adverb modifying a verb phrase or sentence occurs between a verb and its complement. This happens in American English only with the copula, as in:
John is always sad/the worst player.
In British English we also have this order with have used as a main verb:
John has always a good deal to contribute.
Because the grammar tool doesn't contain the copula or main verb have, this evidence is not within its scope.
When an adverb appears between an auxiliary verb and a main verb, this can either be due to adjunction of the adverb to the auxiliary's V' followed by movement of the auxiliary over the adverb to I or be due to adjunction of the adverb to the main verb's V'. Hence, such sentences do not provide evidence for verb movement.
4. Looking only at the variant forms generated by this grammar, is there evidence that English does not have the movement option specified by G2? Again no. G2 allows only lowering, which means that any adverb adjoined to the V' of a verb will appear to its left. When the adverb appears to the right of a verb, that might be evidence for raising but in the cases that can be constructed with the grammar tool, the relevant verb is always an auxiliary so that the same word order can be produced by adjoining the adverb to the V' of the main verb.