Typically, Bladed Brush and Slashing Grace can't work together

The benefit of feat Bladed Brush, in part, says, "When wielding a glaive, you can treat it as a one-handed piercing or slashing melee weapon… for all feats and class abilities that require such a weapon" (emphasis mine). The benefit of the feat Slashing Grace, in part, says, "Choose one kind of light or one-handed slashing weapon…." A creature that possesses the feat Bladed Brush only counts a glaive as a one-handed slashing weapon while the creature wields a glaive; the glaive itself remains a glaive, which is not a one-handed slashing weapon. No matter how an individual creature treats its glaive when that particular creature wields its glaive, the glaive is still an unsuitable weapon choice for the feat Slashing Grace.

Were Bladed Brush not to require actual wielding, and, instead, its benefit started with You can treat a glaive as a one-handed piercing or slashing melee weapon…, it and the feat Slashing Grace would work fine together. Were the feat Slashing Grace not to mandate picking a specific kind of weapon, it and the feat Bladed Brush would work fine together. However, the feats both don't give an inch and remain incompatible.

While this GM can see that a few issues arise were either feat subject to a house rule changing it to make the two feats compatible—their interaction with the magus's extraordinary ability spell combat springs to mind—, I imagine that because of the significant feat investment other styles of play would remain popular. I'd ask the player who pitched the house rule to show me his PC's plan first before I'd consider making such a house rule, though.

Making them work together anyway

To be extra clear, the feat Slashing Grace says, "Choose one kind of light or one-handed slashing weapon" (emphasis mine). However, while this GM views a weapon's kind as the weapon in the abstract—possessing only its printed statistics—, there's actually no formal definition of a kind of weapon. With that in mind, a GM that rules that the feat Bladed Brush changes what kind of weapon a glaive is while the creature wields a glaive gives creatures some options for gaining the feat Slashing Grace (glaive) if the creature's first taken the feat Bladed Brush.

For example, a human fighter that's already a worshiper of Shelyn (the Golarion deity of love and beauty) and that possesses the feats Weapon Finesse and Weapon Focus (glaive) takes at level 1 the feat Bladed Brush. Then, at the end of the session wherein that human fighter gained enough experience points to advance to level 2, if that human fighter is wielding her glaive, she can take the feat Slashing Grace (glaive) as the feat Bladed Brush says that the glaive counts—while the feat's possessor wields a glaive—"for for all feats… that require" a one-handed piercing or slashing melee weapon.

That is, while it's normally impossible to use the feat Bladed Brush to meet the prerequisite of the feat Slashing Grace (glaive), Character Advancement says, "A character advances in level as soon as he earns enough experience points to do so—typically, this occurs at the end of a game session, when your GM hands out that session’s experience point awards." To do this then the character and the player must be aware that advancement is about to occur and the character must be at that session's end in a position to wield her glaive.

This is neither impossible nor particularly shady, but it will typically be unexpected, certainly the kind of thing that should be discussed with the GM beforehand rather than suddenly sprung on the GM.

Likewise, a GM may allow a character like the aforementioned human fighter—if she's not in a position to wield her glaive upon advancing a level or if the GM nixes the character advancement scheme—to use the rules for Retraining to exchange another feat for Slashing Grace (glaive), although the GM may require the character to wield the glaive continuously for five days.

Note: In addition to your Paizo messageboard threads from 2017, 2017, and 2017, there're other threads about this interaction like these from 2016, 2017, and 2017.

You can catch them, but you cannot use them.

Alchemist's bombs cannot be used or carried by anyone else other than the alchemist who created them:

An alchemist’s bomb, like an extract, becomes inert if used or carried by anyone else.

This means you can deflect and even catch a bomb, but you cannot throw it back and expect it to explode (it won't). If you throw it back, expect it to be an improvised throw weapon and cause equivalent damage to throwing a vial or cup of glass at someone (probably 1d2 or 1d3 damage).

This also means that, even if the alchemist creates a bomb and hands it over to a friend so they can throw it, the bomb becomes inert as soon as it is held by another character.

James Jacobs (Paizo's Creative Diretor) also confirms that bombs, being ranged attacks, can be deflected by monks (and whoever has the feat).

The bomb still explodes if deflected, but since it is not directly hitting your character, she takes no damage from it. Normally, missing a bomb would cause at least the splash damage, but the character is protected from the text of Deflect Arrows:

Once per round when you would normally be hit with an attack from a ranged weapon, you may deflect it so that you take no damage from it.

Everyone else within the splash radius should still take damage from the explosion if the bomb is deflected, but not if the bomb is snatched. If a bomb is snatched, it did not hit any target, not even the ground. If there is no direct hit, the bomb doesn't cause splash damage.

A hit deals direct hit damage to the target, and splash damage to all creatures within 5 feet of the target.