The 'r' changes the pronunciation of the following consonant and is not itself pronounced when followed by r, t, l, n etc, turning them into retroflexes.
The way it was explained to me is "uräkta" is apologizing for something that will happen (ex. you need to squeeze past someone) and "förlåt" is apologizing for something that has happened (ex. you bumped into someone).
Do you know that if you don't know the answer of a question, just hover your mouse/cursor over the word you don't know and you will get the meaning of that word
Ursäkta is used by natives as an interjection "excuse me", not as "forgive me". So this phrase makes no sense. It should be "Nej, förlåt" - "No, sorry" (aka. forgive me for the rejection).
This exact sentence often pop up in many other language courses, but I find this one particularly weird. I've never been in a situation where I've used "Nej, ursäkta!" especially with the word no and an exclamation mark.
Ursäkta (mig) will do just fine.