You should split this question into several.
The same debtor can have slightly different credit curves for different products and tiers, eg 1at lien loans, senior unsecured bonds, subordinated... it's normal to have some basis between them.
A CDS curve is a particular credit curve that refers to credit default swaps for different lengths of time.
If Bloomberg knows CDS quotes, then you can see them in CDSW. However Bloomberg probably doesn't know CDS quotes for many obligors you may be interested in. For many obligors, Bloomberg only knows a 5-year CDS spread, since the rest of the CDS curve isn't liquid enough.
CDX NA IG is an index of CDS on a list of North American Investment Grade obligors that seldom default. It is usually quoted as spread, just like a CDS.
CDX NA HY is an index of CDS on a list of North American High Yield obligors that sometimes default. It is usually quoted as price, like a bond.
CDSW helps you convert between spreads, prices, and upfront fees. The conversion is well-documented and relatively simple. The different quoting conventions for different indices don't really make much difference.
There are other CDS indices, also for Europe, Japan, and others. Some are quoted as spreads, others as price, it really doesn't matter as long as you correctly keep track of what the quote means, e.g. don't misinterpret 99 bps CDX IG quote as a price, don't misinterpret 101 (%) CDX HY price as a spread in bps.