(a) The simple infinitive without 'to' is still used, ★ simple infinitive は to のない不定詞のことではないでしょうか？
(b) chiefly after auxiliary verbs, ★ with の方が正解かもしれません。
(c) as in 'He will come,"
(d) for "He is going to come.'
(e) thinking of 'to' as a part of the infinitive ★ e, g, i, j については、ryoutarou さんと同意見です。
(f, g) a prejudice has grown up against separating 'to' from the verb.
(h) why 'to' should immediately precede the infinitive for which it is a sign,
(i) in course of time
(j) used in either an active or a passive sense,