‘ And the man Micah had a house of God (or ‘gods'), and he made an ephod and a teraphim, and installed (‘filled the hand of') one of his sons who became his priest.'
The fact that he at this stage installed one of his own sons suggests that this house of God was new, prepared by him to receive the ‘images'. Both Micah and his mother appear to have been genuinely determined to please Yahweh, although in a way that contributed to their own prestige. But they were clearly not well taught in what was necessary, although having some general idea about such things. The fact that Israel had the Law of God at the central sanctuary did not mean that the knowledge of it was satisfactorily disseminated. And they were influenced by what went on around them.
From now onwards the name of Micah (micyhu) is abbreviated (to micah) in the Hebrew text, dropping the name of Yahweh. This may have been the writer's way of expressing his disapproval of what follows.
They seemingly did not recognise that to have their own house of God, their own ephod and their own throne of Yahweh was contrary to Moses' teaching, and that teraphim especially were frowned on as linked with divination and idolatry (1 Samuel 15:23). Nor, seemingly did they recognise that to have their son as their own family priest was not acceptable, although the fact that when the opportunity came to appoint a Levite, he did so, demonstrates that he was aware of this defect (someone may have pointed it out to him). We must not necessarily assume that the son acted as a full sacrificing priest. His responsibilities might have been limited to using the ephod to discover the will of God and offerings not of a sacrificial kind.
Micah was a religious innovationist and demonstrated how the Israelites were developing forbidden forms of worship contrary to the Law of Moses. They did what was right in their own eyes due to their failure to let Yahweh have His rightful place as King by honouring the covenant and the central sanctuary. To ‘fill the hand' was to appoint as priest - Numbers 3:3. We note that David also appointed his sons as priests, but this would be as priests of the order of Melchizedek in Jerusalem, as recognising their authority there, but not as sacrificing priests (2 Samuel 8:18).
The ephod was a priestly metallic robe worn by ‘the priest' in the Tabernacle which among other things was involved with the Urim and Thummim (Exodus 28:30; Numbers 27:21), which were used for discovering the mind of Yahweh. In the case of Laban, teraphim were described as ‘gods', divine objects (Genesis 31:30 with 35). But they were used for divination (2 Kings 23:24; Ezekiel 21:21). Otherwise we know little about them. Thus Micah was wanting to doubly ensure that he could discover the mind of Yahweh, although his means were unacceptable to the pure Yahweh worshipper.
In all this there is no mention of an altar. Worship in this house of God may well have been by offering other things than sacrifices.
Micah and his mother would have been familiar with the idol shelves found in Canaanite houses, and which soon found their way into some Israelite houses. They were seeking to have something similar but dedicated to Yahweh. But such was the state of Yahwism, of the central sanctuary and of the teaching of the Law at the time, that they did not realise that they were doing wrong. Yahwism was at a low ebb.