Not sure about 2 but he was definitely in heat.
Geez his ovulation is insane then
Yes to #1
And #2 half yes. The dominant alphas can lose their memory of their rut if they don't release their pheromones through regular intercourse. Similar to what Keith experiences in the OG story (kiss me liar)
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1. Iirc he didn't beg. He didn't know he'll get pregnant to the point of being marked. Bur them doing the did is with his consent. It's like all bottled up feeling poured out that night unknowingly so he went on with his desires.
2. Yes, Chase was in a rut. From what it seems those in rut don't remember what actually happened during those days. I'm just basing this with what happened with Keith and he was in rut when he was marked by Yeonwoo and he didn't remember who did that. Though at some point, Chase kinda have some nights when he dreamt of Josh not knowing it was their night together. Also he looked for the person he was with that time although for him that happening to him is just like close to 0.01% chance as he basically believed he slept with a dog showing his trauma.
1. Why did the bottom begged to be creamed? Was he in heat or was it just him being dumb?
2. Was the alpha in rut? If so in this universe does the alpha not remember the nights of their ruts?