@Chris O'Halloran Welcome to Denver man! Denver is a fantastic place to invest.
The BRRRR strategy is very challenging to accomplish here due to finding deals that work since a lot of local investors are fine buying fixer uppers for expensive prices. When the worst house on a block sells for 400k and the best house sells for 500k, it doesn't leave you much room to work with.
Basically, you will have to build relationships and find off market deals since that will be your best bet if you are looking to BRRRR.
Congrats on getting your Social Security # and establishing credit, check to see if it is possible to house hack by talking to a lender. It is easily the best strategy to maximizing returns while living in the property and eliminating your housing costs and sometimes make money living in that property depending on where it is located and number of bedrooms and bathrooms, etc.
Also, you have a competitive advantage with your background as a carpenter which will serve you will if you do all the improvements yourself.
To answer your questions:
1) Depends on the county, but most places if you pass a homeowners exam, you can do a lot of work yourself and pull your own permits.
2) It is always a good idea to permit everything since whenever you sell it , you want to disclose that, and it will give peace of mind for most future buyers. The only things that can be done without permits are when you are doing demo that's not structural, simple improvements (adding cabinets), like for like (ie. replace light fixture with new light fixture), but everything else is fair game depending on the county since they all want to collect permit fees.
3) In my opinion, the best areas in Denver are west Denver neighborhoods (Villa Park, Barnum, Valverde, Westwood, Athmar Park and Harvey Park. Also, the cities of Westminster, Arvada, Thornton, Northglenn, and Lakewood.
Those neighborhoods and cities are probably the last affordable markets for both BRRRRs, fix and flips, and house hacks since you can get more house for less price relative to the "popular" parts of Denver like SLoan's Lake, Highlands, Berkeley and Sunnyside and downtown. You can easily find high quality houses in those neighborhoods for 400-500k.
4) For loans, if you are looking to do just BRRRRs, I would talk to hard money lenders such as Pine Financial, and you are looking at 10-12% interest rates for those while you are under construction and then refinancing into a normal conventional loan.
For house hacks, since you will be making it a primary residence, you can get a FHA 3.5% loan and a conventional 5% loan fairly easily.
Since you have an advantage with your background and ability to buy materials at a discounted price, you have lots of potential strategies. BRRRRs are definitely the hardest because you have to be able to find beat up properties off market, close with cash or a hard money loan or partner with someone that has the capital, fix it up, find tenants, refinance, and then repeat. Not impossible but the ones doing it in Denver have great off market deal marketing strategies and deep pockets to make it happen.
House Hacks are the easiest since you are usually finding properties that don't need a lot of work, putting only 5% down and then saving on living costs while building equity, cash flow and getting tax benefits.
You could combine both strategies and do a BRRRR house hack by moving into a house that needs a lot of work and you can add value by adding bathrooms, bedrooms and remodeling the kitchen and then refinancing to pull your money out, but again, it is a tougher strategy since most house hacks are livable condition.