Hi,
1. Lipid solubility or lipophilicity is one factor that aids diffusion through the phospholipid bilayer, but it is not the only one.
--- A small molecule of lipid as against larger ones [like palmitic acid or stearic acid], pass through more easily [as can small ions [which are not lipophilic, so the converse applies] to a certain extent, although most have special mechanisms that permit active transport]
--- Uncharged particles pass through the membrane more easily than charged ones as uncharged molecules tend to be more polar.
Certain drugs e.g. topical eyedrops are formulated to possess both a lipophilic and a hydrophilic part, so that they can cross both the lipophilic corneal epithelium [and endothelium], and the hydrophilic corneal stroma, respectively [the cornea consists of five layers: from the outside going in: epithelium, Bowman's layer [basement membrane of the epithelium], stroma, Descemet's membrane, and endothelium].
2. The protein channels are part of the structure of the membrane [here integral proteins] so although they are somewhat flexible [fluid mosaic], they do not need to "cut across".
Hope this helps & be safe!
M.