Basic items drops - with/without MF

You're actually looking at multiple different mechanics there.
If you really wanna go into full detail, see something like https://diablo2.diablowiki.net/Item_Generation_Tutorial

But generalizing/summarizing (and simplifying) a bit (a lot)..
Item quality in D2 exists in a range from high to low: unique -> set -> rare -> magic -> superior -> normal -> low quality

When an item drops, as one of the earlier checks, the game determines the item's quality within the above range (so far as applicable). This is effectively one 'step' and is affected by your MF. So yes, higher MF lowers odds of both, normal and superior bases.

Ethereal is an entirely separate check as each item simply has a 5% chance of rolling ethereal. This applies to uniques just as much as it does to normal bases. The exception being items that cannot by definition roll ethereal (set items, items with an 'indestructible' affix, ...). Your MF has no impact on this.

"Is it socketed?" is only rolled for superior or below items with 1/3 odds of them getting sockets. The actual number of sockets (if the prior check said "yes, it gets sockets") is then rolled separately within the allowed range. For other items (magic, unique, ...) whether or not they roll with sockets is determined by their affixes and not subject to a random roll. For these, too though, they may allow a range of sockets in which case the actual number of sockets is still a separate roll. Your MF has no impact on this either, other than the impact it had on getting a superior or below item to begin with.