Most masks and hoods I’ve worn are too baggy and move around or get stretched out eventually.
I have a couple pairs of these Under Armour ones for me and my girl. They are tight and never stretch. UA Tactical Hood
Yes. I will usually wear a balaclava such as the one below.
Under Armour Unisex-Adult HeatGear Tactical Balaclava https://www.amazon.com/dp/B00RWF2Q8A/ref=cm_sw_r_cp_api_i_0FEqFbXR3B96A
Frankly you sweat like mad anyway in that kind of heat. It does provide some evaporative cooling as it fills with sweat a bit then gets cold when it evaporates away. Mine isn't silk though. It's basically this guy only it wasn't $50. I'd bet one of the Chinese $10 masks would work equally well to evaporate away moisture in heat.
As for suffocating, again, warm weather balaclavas should provide some ability to breath through them. Not all are created equal though and you'll likely find that breathability varies. I also have some 'buff' type sleeves that are fine enough, but breathing through them for even a short period of time causes a lot of moisture inside it which is far from pleasant. I opted for a cheap multi pack though so it could just be an inferior material blend. You can fold those guys up into a balaclava shape too though and ultimately I would guess they could be more versatile.