Great questions! Your 3 questions can be answered in 2 parts:
1. How do small, uncharged gasses (ie: O₂, N₂, CO₂) diffuse through lipid bilayers?
First it's important to clear up some terminology: Absorbing a compound isn't the same as being permeable to that compound. If you say that a compound is absorbed (or partitions) into a bilayer, you're assuming that the absorption of the given compound by the bilayer increases the entropy of the system (and is thus energetically favorable). For example, lipophilic compounds partition into lipid bilayers because of the hydrophobic effect; by partitioning into the bilayer they break a number of hydrogen bonds and thus increase the disorder of the system.
Small, dissolved gasses like O₂, N₂, and CO₂ are not absorbed into lipid bilayers, they simply diffuse through passively because of their small size and because they are non-polar.
Water is also able to passively diffuse through a lipid bilayer even though it is polar. We might think it should be fairly rare for a polar water molecule to pass through the hydrophobic center of a lipid bilayer, but typically living cells are found in aqueous environments, where concentrations of water outside the cell are extremely high, so this does occur at biologically relevant rates. In fact, the passive diffusion of water in and out of cells is so important that many cells have developed special transmembrane proteins to facilitate the passage of water in and out of cells (most notably aquaporins and pressure-gated channels).
2. How do non-polar molecules pass through lipid bilayers?
This is answered in the related question posted in the comments section of your question. Briefly, it has to do with the same electrostatic problem I mentioned above: Though there is an energetic cost for non-polar compounds to pass through the hydropilic layer of a lipid membrane, in most cases the partitioning of the compound into the membrane still raises the overall entropy of the system (due to disruption of the hydrophobic effect), making it an energetically favorable process.
It should be noted that for the most part, polar compounds do not spontaneously cross cell membranes because of the hydrophobic region of the lipid bilayer. When passage of these compounds into or out of the cell is required for life, cells typically produce transmembrane proteins which can act as either active or passive transporters to allow these compounds through.