First problem happens when engine is cold

First problem happens when engine is cold. Second problem happens randomly and intermittenly.
but I think they are both related.

first problem.
2-5 seconds after acceloration, the engine bogs down to about 100-200 rpm. And sometimes dies. But most of the time as long as I step on the gas a little harder, after 1-2 seconds it goes right back to normal acceloration as if nothing happened.

second problem
this happens randomly. I cannot pinpoint any conditions it happens more or less under. But if feels sluggish at times. For instance ill try to accelorate to speed up, (rpms seem normal for how much/little im pressing the gas) but it will feel like im not pressing on the pedal at all. Sometimes it takes as much as a full minute to get from 15-70 (getting on the freeway)