The spell effect would be unchanged.

In DnD 5e spells only do what they say that they do or to put it another way - 'there are no secret rules'.

Any spell can be cast using a higher level spell slot than necessary - so you could cast Find Familiar using a ninth level slot. But the Find Familiar spell doesn't tell you that there would be any additional affects from casting at higher levels - so there wouldn't be any.

Contrast that with spells like Magic Missile (as you suggested) which states explicitly:

At Higher Levels. When you cast this spell using a spell slot of 2nd level or higher, the spell creates one more dart for each slot level above 1st. (SRD p. 161)

If a spell doesn't have this 'At Higher Levels' section then there are no change to the spell effects from casting it at a higher level.

There are, however, a couple of incidental benefits from casting a spell at higher level:

• Your spell will be harder to counterspell than normal (if cast at level 4 or above).
• You are still able to cast the spell even if you've run out of low level spell slots.

P.S. The above is the RAW answer to this question and it's what I'd tell my players if they asked.

That said, I have been left pondering if adding some homebrew effects for an NPC villain might be rather fun? You could rule that by casting Find Familiar at ninth level your villain received nine separate standard familairs, or one familiar nine times as strong as usual. Either option could be an interesting character facet for an antagonist.

Magic Initiate: No

Having the Feat 'Magic Initiate' does not grant the character an additional class. Since the rule for spell scrolls is:

...if the spell is on your class's list...

The character would still not have the spell in its class list if it did not before the Feat.

Ritual Caster: No

A ritual caster can only cast spells from their ritual book. The Spell Scroll can be used to add a new spell to the ritual book, but don't forget more of what Ritual Caster says:

The spell must be on the spell list for the class you chose, the spell's level can be no higher than half your level (rounded up), and it must have the ritual tag

It seems that the Ritual Caster is a more specific rule than the generic rule about Spell Scrolls, so it follows the player can use the spell scroll to add a new ritual long as you follow all the rules of the Ritual Caster.