2004 Vauxhall Astra everything :(

First bought the car in may , was going fine , until 2 weeks ago I went out in the morning to start it, yes I gave it time to heat up ,stopped engine for few mins and back in again ( was doing the school run) car wouldn't start ??? So I replaced the battery thinking it wasn't getting the correct amp (Bosch) I went to Halfords bought a higher voltage although it's not a Bosch this time lol !! And still the same , jumpt it with leads done the lead test with the alternator!! Didn't cut out .... headed to a friends house or tried to. Was going round the round-about and the power steering just went , and boy this b**ch was hard to get back round and head bk home with this pump kicking in and back out with the battery light on and engine management light?? , meaning I was gettin powering steering then arms like pop-eye!! So I just bought a steering pump (2nd hand) put it on tonight gave it a small run round the street , so heading out to the car to head home I was turning and felt the steering go on me again pop-eye arms and the dash lights dimmed!!

Please help me before I go spend more cash on an alternator :/ any opinions welcome as I'm at my wits end and I need this car for the job I'm in