You Can!

If a character possesses an alignment that's Lawful Good, one step away on each axis means as a far away as Neutral for the Lawful component of Lawful Good, and as a far away as Neutral for the Good component of Lawful Good.

Here's the chart of alignment steps. While the text reads

that diagonal "steps" count as two steps. For example, a lawful neutral character is one step away from a lawful good alignment, and three steps away from a chaotic evil alignment.

the feat Improved Familiar reads

You may choose a familiar with an alignment up to one step away on each alignment axis (lawful through chaotic, good through evil).

Emphasis mine. Neutral is one step from Lawful on the L/N/C axis while Neutral is one step from Good on the G/N/E axis. Thus taking both steps along both axes allows a LG character to select a N improved familiar, despite the text's 2-step diagonal rule.

Yes, all items implicitly allow saves for effects that mimic spells with saves.

Aura faint enchantment; CL 3rd

Slot ring; Price 10,800 gp; Weight —

Description

A ring of animal friendship always bears some sort of animal-like design in its craftsmanship. On command, this ring affects an animal as if the wearer had cast charm animal, causing the animal to regard the wearer as a trusted friend.

In Saving Throws Against Magic Item Powers, we see that:

Magic items produce spells or spell-like effects. For a saving throw against a spell or spell-like effect from a magic item, the DC is 10 + the level of the spell or effect + the ability modifier of the minimum ability score needed to cast that level of spell.

Staves are an exception to the rule. Treat the saving throw as if the wielder cast the spell, including caster level and all modifiers to save DCs.

In the case of this ring, is casting a level 1 spell, at caster level 3. This gives you all the information you need to calculate spell save DC (10 + 1 + 0 Wis bonus from Wis 11 = 11) and SR checks and dispel DCs and the like.