SurpriseBub, I can't comment on the bottle but, certainly on the breast, a baby will cough/splutter/choke when you have a 'let down' as the flow is much faster - mine certainly does! This can happen more than once a feed and you may feel a tingling sensation when you have one (although some mums don't feel anything). Laying back can help as gravity slows the flow but once your supply regulates around 4-6 weeks, it should happen less and less.
All babies have reflux to a degree as the valve at the top of the stomach (I think) is open until around six months so some of the contents can easily flow back up. Spitting up isn't usually a medical problem unless baby is projectile vomiting, in distress and not gaining weight or having sufficient wet and dirty nappies.
I suppose with the bottle, if baby sucks hard on that like they do on the breast that could make them choke because the milk comes out quite easily?