Regarding liquid helium, reference is made to party supply stores and to the national reserve. Both of those sources have helium as a gas. The really hard part of making liquid helium is not obtaining the gas but getting it cold enough to liquefy (about -269 degrees C). And because no container is perfectly insulated a tank of liquid helium will warm up and boil off in just a few days.
A Mexican standoff was traditionally meant to describe a situation whereby none of the parties involved could act without triggering their own demise, nor could they choose to walk away without consequences. The Cold War is a good example of a classic Mexican standoff, even though it involved only two parties. Later definitions are mostly derived from cinema where a Mexican standoff usually involves at least three parties pointing firearms at one another.
This is the third time that the guys enlist the help of one of Howard's shady connections, after the guy who checked out the worth of The One Ring on the black market in The Precious Fragmentation (2010), and the guy they wanted to buy scalped Comic Con tickets from in The Convention Conundrum (2014).
Disguising the helium tank as "Uncle Harvey" is a reference to Harvey, the giant invisible rabbit from Harvey (1950). Jim Parsons was once in the stage play this film was based on.
Chuck Lorre must have really liked the parking garage scene. In just four months a very similar scene plays out in Sticky Hands and a Walk on the Wild Side (2016) - except in Mom it was Canadian Maple Syrup instead of helium.