Hi, I can help you with this.
Before we get started I'd like to point out that a Professional Engineer's standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for informational purposes only (general sizing and budgeting) and is based on the information provided by you. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.
Please let me know if you're still interested in proceeding. If so, please let me know your zip code, so I can look at snow loading.
You can plan for a W8x31 ASTM A992 Gr. 50. It's 8" deep and weighs 31 pounds per linear foot.
That's a pretty big typo. Are the dimensions of the addition correct?
What is the actual span of the beam and what is the length of the rafters on each side of that beam?
No problem. Please make sure to have this reviewed by a licensed PE once you have everything finalized and make sure the posts, foundations, and connections are designed and detailed.