Ford KA electrical issues

I had the bonnet up checking the oil n water. Could just b a coincidence but when that was done n I drove it for the first time the car started to judder in low gear, but as the speed got up it would stop. Then, as well as that, if I had to change into a low gear I noticed the petrol, mph n rev gadges would drop n the radio would cut out, then everything would return to normal when gaining speed. Then my headlights and full beam blew. I got the bulbs replaced but they went again later that day. The battery light has come on a few times but gone out a minute later; Halfords checked the battery n it's ok. I've had no problems starting it. I know everyone is thinking Alternator, but when I bought the car a few weeks ago I was told that the fan belt needed to be replaced. Everyone I've asked have been stumped and I was told that this engine doesn't have a fan belt. Please help. I'm skint n so scared to take it to a garage where I'll get ripped off as I'm female.