Hello and welcome spoiler,

I am still a new member here, but the best advice I can give you is follow the "Index of Crossfire Problems" link at the bottom of VALK's signature. Onehundred80 took the time to group many fixes/problems into categories with PDF links. I spent about 2 weeks reading all of them and making a list of "issues" that had to be addressed immediately.

The no start issue you are having - you may want to give a little more information. If the starter is cranking, but the engine is not catching that could be a different issue than not cranking at all (could be the Crankshaft Position Sensor). I would definitely repair the RCM as that is a very common problem.

Item 6: There is a link in the electrical section for the factory alarm battery change that you might need to utilize. To answer your question directly - your factory alarm will not chirp unless the siren module has been replaced/upgraded.

Item 8: I bought a custom sunshade off of Amazon that fits well:
For your check engine light, if it is on now - get it read free at an auto parts store (O'Reilly's does it here). Once you have the code(s) do a search on this forum and there is usually information and solutions. I hope it is just a loose gas cap, but it would be best to check and verify prior to replacing anything.

Best of luck!