[ Chevrolet ] Open Question : Chevy s10 3 door extended cab problems?

i have a 1998 Chevy s10 3 door extended cab that has two concerning problems. 1) when i try to accelerate from a stop it chugs and when it shifts to second the tires break loose very briefly. i dont know why it does this. im hoping it is not a transmission problem but i have noticed the fuel pump makes an odd whizzing or buzzing noise. and 2) when i shift from drive to reverse or visa versa it has some give in it where i need to let it rock foreward or back to be sure it set in otherwise it jerks violently. does anyone know anything about either of these two problems?