Help with Next Steps in the Buying Process

First time new car buyer trying to do things right. I had my current car serviced last weekend (2012 Prius). Out of curiosity, asked them to give me estimate of trade in value. They quoted 7k, and immediately texted me some numbers on different new cars.

I'm including a link for a screenshot of the one I'm considering (Corolla Hybrid).

I did a test drive today and was happy with it but did not start any negotiating. Just told him I would be in touch.

I don't want the tint and premier protection but I DO want the premium package that is listed on the website as $1,135.

• Should I assume they will actually give 7k since it's on the payment sheet in the screenshot? Or is that just to get me back in the door?
• Can I just offer to add the premium fee I want and they remove their tint and protection fee? Just swap them?
• Should I send this screenshot to other dealers to see if they can beat it? I'm pretty happy with the OTD price but maybe it's worth shopping around?
• What should my next step be in the negotiation process?
• What should I do to get the best loan terms (my credit is in the mid 700s)?

Screenshot of the numbers from dealership: https://imgur.com/a/4d3NHEn

Thank you!