There's no reason to believe P1 has advantage in this scenario
Unless there was any reason why an attack would have advantage, such as if the enemy had been hit by guiding bolt or if P2/3 had taken the Help action, then there's no reason to think that P1 should have advantage due to the positioning of the combantants.
As Thomas Markov's answer points out, the optional flanking rules require you to be adjacent to the enemy to gain advantage, which P1 was not (they were 10 feet away). That said, as a DM, you could rule that reach weapons count as being adjacent for the purposes of flanking if you wish to do so (at least if it's just 10 foot reach, since that could get silly otherwise).
The positioning of P2 would not interfere with having advantage or disadvantage, but might give the enemy cover
Whether or not someone else is in the way should not, by itself, grant advantage or disadvantage. However, a DM might rule that P2 being "in the way" might grant the enemy an increased AC due to the rules on cover.
The prone P2 would of course create less cover for the enemy than a not-prone P2. Some DMs might rule that a prone P2 grants no cover (which is what I'd rule), whereas others may grant half-cover (+2 AC) to the enemy. Once P2 gets up, some DMs may rule that the enemy has either half- or even three-quarters-cover (+5 AC).
Further reading: Do prone creatures provide cover?