Here you can hear real people saying jag är en ung kvinna ... http://el.forvo.com/search/jag%20%C3%A4r%20en%20kvinna/sv/
Here's a good resource for anyone working through pronunciation issues. Can't guarantee it will have every word, but sometimes you can search a word and even see some phrases you might find it used in.
For example, listen to "Jag" here.
They are both correct. In English, all verbs change depending on who they apply to. Most only change by having an 's' on the end (eg: I walk, he walks, etc).
The verb 'to be' is slightly more irregular and has 3 forms in the present tense: I am; you/we/they are; he/she is. They all translate to är.
Sorry, I'm new here, but on the exercises before this, the "j" is pronounced as the voiced palatal approximant (as in "y" as in "yes"). But the "j" here sounds like the voiced palatoalveolar fricative (the "j" in French "je"). Is there a pronunciation rule I have yet to unravel?
One of the contributors (devalanteriel) shared the link with me, the Swedish pronunciation videos channel